Table of Contents

OPERATIONAL AMPLIFIERS III

THE RETICON R5620 PROGRAMMABLE FILTER IC

A TUNABLE AUDIO NOTCH FILTER USING THE RETICON R5620

THE SMITH-KETTLEWELL TRAINING AID FOR PIANO TUNERS

THE SMITH-KETTLEWELL AUDIBLE STROBE TUNER

EDITORS CORNER

OPERATIONAL AMPLIFIERS III

By Albert Alden

Introduction

So far, we have described op-amp circuits which, with the exception
of the "active diode" circuits of the last installment, have only used
resistors as scaling elements. Capacitors and inductors may also be
used. Inductors tend to be bulky, expensive, and often depart from
the ideal. This, and the fact that an equivalent circuit can be
designed using capacitors, essentially eliminates inductors from
consideration in op-amp circuits. The op-amp circuits described in
this installment utilize capacitors and resistors to make a class of
circuits referred to as active RC networks.

Capacitors

The relationship between the voltage across and current through a
capacitor is I equals C times the derivative of the voltage with
respect to time. The derivative is the instantaneous rate of change
of the voltage in units of volts per second. Thus, the current
through a capacitor equals the capacitance times the rate of change of
the applied voltage.

The above relationship can be rearranged to give voltage as a
function of current. This becomes

E = (1/C) ∫Idt

(or E equals 1 over C, that fraction times the integral of the current over time).

This means that the voltage across the capacitor is equal to the reciprocal of the capacitance times the integral of the current with respect to time. The integral function
may be thought of as a running summation of the current. This works
out to be equal at any instant to the charge "q" accumulated in the
capacitor since the start of the integration period.

The above two relationships represent two operations which may be
performed on a signal to obtain additional useful information. For
instance, if we have a signal proportional to the velocity of a
device, the derivative of the velocity signal yields a signal
proportional to its acceleration, and the integral gives the
displacement from the starting of the integration operation. Note
that integration has to have a starting point.

Using just a capacitor for these two operations requires a voltage-
to-current or current-to-voltage conversion to have the input and
output as voltage signals. The op-amp will do this for us.

Op-Amp Integrator

The circuit is as follows. An input resistor
(R_i) is connected to the inverting input of the op-amp. The non-
inverting input is connected to ground directly (or through a resistor
equal to R_i to eliminate bias current error). An output capacitor
(C_o) is connected from the output of the op-amp back to the inverting

input. If we apply a positive voltage (E_i) to the input resistor, a
current I = E_i/R_i flows, since the inverting input is at
virtual ground. The op-amp, in order to keep the inverting input at
0V, has its output go in a negative direction as required to accept
the current flowing through the input resistor. The relationship

between output and input is

E_o = -(1/(R_iC_o))∫E_idt

(or E_o equals the quotient of one divided by the product of R_i times C_o, the negative of that quotient times the integral of E_i times dt.)

For example, if R_i is l megOhm and C_o is 0.5 microFarads, then for
an input (E_i) of 1 volt, the output will be a negative-going ramp
which will be minus 2 volts after one second, minus 4 volts after two
seconds, etc.

Integrators usually have a reset switch across the capacitor which
is opened at the start of the integration. If one desires to hold the
output signal at the end of an integration period, the input should be
opened and/or shorted to ground with a switch. Mechanical switches or
relays may be used where speed is not important; otherwise, analog
switches such as the CD4053 are excellent for this application. The
CD4053 is controlled with digital signals and can switch analog
signals of either polarity.

Both input offset voltage and input bias and offset currents cause
the output of the integrator to drift. Bias current error is
eliminated, as explained above. Using an FET input op-amp and nulling
the input offset, as described in the last installment, will reduce
the drift.

The input-output relationship for an inverting amplifier, Eo = -E_i (R_o/R_i), is a special case of the general expression E_o=-E_i (Z_o/Z_i).
Z_i and Z_o are the impedances of the input and output elements. These
may be resistors, capacitors, inductors, and any combination thereof.
The output element of the integrator is a capacitor, a device whose
impedance is inversely proportional to frequency. Therefore, the
frequency response of the integrator circuit is the same, since the
impedance Zi of the input resistor is constant, leaving Zo as the only
frequency-dependent term in the above equation.

Op-Amp Differentiator

By interchanging the input resistor and
output capacitor in the integrator circuit, we get a differentiator.
When applying a time-varying voltage to the input capacitor, a current
proportional to the instantaneous rate of change (expressed in volts
per second) flows to the virtual ground. The op-amp output voltage
goes negative to accept this current, such that E_o = -I times R_o.
This expression, combined with the voltage-current relationship for
the input capacitor, gives E_o = -R_o C_i (dE_i/dt).

Given a C_i of 0.5 microFarads and an R_o of 1 megOhm, applying a ramp
input of 1 volt per second will result in an output of -0.5 volts.

Op-amp offset voltage and current errors don't cause drift as with
the integrator, but only a constant offset error in the output.

Z_i for the differentiator is that of the capacitor. This results in
a circuit whose frequency response increases proportional frequency.
This causes two problems for the op-amp differentiator. First, high-

frequency noise is emphasized (like having a treble boost); second,
the phase shifts of the external components and the internal op-amp
frequency compensation add so as to approach l80 degrees at a
frequency where there is sufficient gain to cause oscillation. By
putting a resistor in series with the input capacitor, the input
impedance Z_i is prevented from going below the value of the resistor.
The frequency at which this occurs is equal to

1/(2π RC_i)

(or 1 divided by the product of 2 times pi times R times C_i).

Above this frequency the differentiator turns into an inverting amplifier. R should be chosen
to match the bandwidth of the signal you wish to differentiate.

Putting a capacitor across Ro will give additional filtering. The
formula is the same, with the R and C now being the components
comprising Z_o.

Filters

We will describe two low-pass and two high-pass filter circuits
without delving too deeply into the general subject of filters. (It
is anticipated that there will be a future series of articles on
filters.) [Note: The single-order filters were described briefly in
the last installment. More detail will be given here.]

Single-Order Low-Pass

This filter passes signals of frequencies
below a cut-off frequency and attenuates signals above that frequency.
The attenuation of a single-order filter is such that the ratio (E_o/E_i) is proportional to the frequency ratio (F₀/F), where F₀ is
the cut-off frequency. This is equivalent to -6dB per octave.
The response (E_o/E_i) at F₀ is -3dB, or 0.707 times the low-
frequency gain. This is a common definition of the cut-off or
"corner" frequency of a filter.

The low-pass filter consists of an input resistor R_i going to the
inverting input, and an output resistor R_o with a capacitor C_o in parallel from the inverting input to the output of the op-amp.

F₀ = 1/(2πR_oC_o),

(or F₀ equals 1 divided by the product 2 times pi times R_o times C_o)

and the low-frequency gain is equal to R_o over R_i. In terms
of Z_i and Z_o, Z_i = R_i, and Z_o = R_o in parallel with C_o.

Single-Order High-Pass

The high-pass filter passes signals of
frequencies above the cut-off frequency and attenuates signals below
the cut-off frequency. For signals below F₀, E_o/E_i is
proportional to F/F₀ (the inverse of that for the low-pass
filter). The response at F₀ is -3dB, or 0.707 times that of the
high-frequency gain.

The circuit consists of an input resistor R_i and input capacitor C_i
in series going to the inverting input of an op-amp. An output
resistor R_o goes from the inverting input to the output of the op-amp. Z_i = R_i in series with C_i, and Z_o = R_o.

F₀ = 1/(2πR_iC_i)

(or F_O equals 1 divided by the product of 2 times pi times R_i times C_i).

The
high-frequency gain is equal to (R_o/R_i).

When capacitively coupling op-amp amplifier stages, the coupling
capacitor constitutes C_i of a high-pass filter. Its value should be
picked using the above formula.

To limit the bandwidth of an op-amp amplifier stage in a circuit,
use the Z_i of the high-pass filter and the Z_o of the low-pass filter,
picking the resistors for the band-pass gain required and picking the
capacitors for the frequency limits desired.

Both the low-pass and high-pass filters can be made with only
passive components (a resistor and a capacitor). The use of the op-
amp gives a filter which has several advantages: the filter can be
designed with gain, the output impedance is low, the input impedance
can be made high, and several stages can be cascaded without each
stage loading and affecting the performance of the others.

Second-Order Filters

We will describe here a low-pass and a high-
pass second-order filter. The operation of a second-order filter
differs from the single-order filter in a couple of ways.

First, there are two parameters to be chosen: (l) a cut-off
frequency F₀, and (2) a parameter which controls the shape of the
frequency response for frequencies near F₀. This latter parameter is
either expressed as the quality factor Q or the damping ratio. The
values of these are related such that either is equal to one-half of
the reciprocal of the other.

Second, the response of a second-order low-pass filter (E_o/E_i)
above the cut-off frequency is proportional to (F₀/F) to the second
power. This is equivalent to -l2dB per octave.

The filter chosen to be discussed here has for Q a value of 0.707.
(The damping ratio happens to also be equal to 0.707.) This value of
Q for the second-order filter results in a response which is referred
to as being "maximally flat." Also, its gain at F₀ is minus 3dB, or 0.707.
It is called a Butterworth filter, after the author who first
described such a filter characteristic in l930. The actual circuit we
will use is called a voltage-controlled, voltage-source (VCVS) filter.
Its attributes are simplicity of construction (few parts) and
simplicity of design (easy calculation of component values).

Low-Pass Circuit

The circuit is as follows. Two equal resistors
(R) in series go from the input to the non-inverting input of an op-
amp. The op-amp is configured as a follower; i.e., the output and the
inverting input are tied together. A capacitor (C) goes from the non-
inverting input to ground, and a capacitor with a value of 2 times C goes
from the op-amp output back to the junction of the two resistors. The
output of the filter is the output of the op-amp. The correct value
of Q (0.707) is taken care of by the ratios of the component values
and the closed loop gain of the op-amp (plus l). The formula for F0
is

F₀ = 1/(2πRC √2)

(or F₀ equals 1 divided by the product 2 times pi times R times C times the square root of 2).

High-Pass Circuit

The operation of the second-order high-pass
filter has a similar relationship to the second-order low-pass as the
single-order filters had to each other. The response below F₀ is
proportional to (F/F₀) to the second power. The gain at F₀ is
-3dB, or 0.707 times the high-frequency gain.

The circuit is like that used for the low-pass, but with the R's and
C's rearranged. Two capacitors in series, each with a value of C, go
from the input to the non-inverting input of the op-amp. A resistor
with a value of R goes from the output of the op-amp back to the
junction of the two capacitors. A resistor with a value of 2 times R
is connected from the non-inverting input to ground. The op-amp is
again configured as a follower with a gain of plus l. The formula for
F₀ is the same as for the low-pass filter.

General Comments

Here are a few general comments which apply to the circuits
described in this article.

Op-Amps

While not mentioned explicitly, it is assumed that you will
make the power connections and add the frequency compensation

capacitor if required for all of the above circuits. For op-amps used
in filters, the open loop gain in the frequency range of interest must
be sufficiently large to get performance approaching theoretical. Op-
amp filters are best suited for audio frequencies.

Capacitors

Film capacitors (polyester, polypropylene, polystyrene,
and polycarbonate) should be used for the best performance from the
circuits we have discussed. Ceramic capacitors are OK for less
critical applications. Avoid using tantalum or electrolytic
capacitors.

Scaling

Filters and other circuits using capacitors and resistors
as frequency-determining components may be scaled in the frequency
domain by changing all of the resistors and/or all of the capacitors
by the same ratio. The frequency is changed by a ratio equal to the
reciprocal of the resistor and/or capacitor value ratio. For example,
if we design a l00Hz filter with l00K resistors, changing to l megOhm

resistors gives us a l0Hz filter with the same characteristics. This
principle can be followed for first order, second order Butterworth
(or not), high-pass, low-pass, etc. Also, the time domain response of

the circuit will change by a factor proportional to the ratio of the R
or C change. For example, by increasing the resistors by a factor of
l0, the circuit will take l0 times as long to respond to a given
input.

Asymptotes

The description of the frequency responses given for the
various filters are those of the asymptotes--that is, these are the
limits which are approached below and above F₀. At one or two octaves
(F/F₀ = 2 or 4) above or below F₀, the actual response is
quite close to that described in this article. In between, the
response moves smoothly from one asymptote to the other. For a
single-order filter, this is fixed. For the second-order filter, this
is determined by Q.

THE RETICON R5620
PROGRAMMABLE FILTER IC

Abstract

This IC contains a 2nd-order
audio-frequency filter of the "switched-
capacitor" type. Its critical frequency is
easily tunable over a wide range; not only is
it determined by the frequency of an applied
clock signal, but the ratio of the filter's
frequency to that of the clock is set by
imposing a binary number on five input pins.
In addition, the "Q" can be set by imposing a
binary number on another set of inputs. Two
example circuits (a notch filter and a band-
pass filter) can be found in the two articles
to follow, "A Tunable Notch Filter," and "A
Training Aid for Piano Tuners."

There are other filter chips using the
"switched capacitance" technique; Reticon
makes a dual 2nd-order filter in their R562l
and a quad filter in the R5622. National
Semiconductor also has a line of such
devices. However, the R5620 is unique in
that it is digitally programmable; the other
devices use external resistors to set the Q
and the ratio of clock to the filter's critical frequencies.

A full discussion of filter theory (including the necessary math for cascading
filters, etc.) will not be attempted here.
A complete package of "all you'll ever need
to know" would indeed be an undertaking, and
the discussion of this nifty little filter
chip would get lost within it.

Heavy Theory

Use of the R5620 is so simple as to be
trivial--hook it up as shown, and it will do

as an obedient black box should. The discussion of its innards is a moral obligation
on my part to you; you deserve nothing less
than having access to the full story.
There's no way around it, however, this is
university level stuff--including some
calculus--and you have my permission to take
it or leave it as you wish. [My profound
thanks to Al Alden, John Brabyn, and Jules
Madey for working through this section with
me, and for making it possible to re-live my
analog computer class with vivid realism.]

Part I
The Analog Simulation of a 2nd-Order System

Analog computers (heavily used from the
l950's on into the early l970's) were the

scientist's Tinker Toy set by which electrical "analogs" of physical systems could be
built and tried. Automotive suspension
systems, airplane wings, and earthquake-proof
buildings were all simulated on analog computers first before actual models were built.
In this way, necessary changes in the actual
designs could be anticipated by adjusting
potentiometers on the analagous electrical
version, after which the tried and true
physical system could be built on the basis
of its computer simulation.

Once a proposed physical system is expressed in terms of its mathematics, it can
be simulated electrically on an analog computer. An analog computer set up to solve a
basic 2nd-order differential equation was
contained in the 5620 chip. The operation of
the filter can be explained by describing two
simulated systems: the first is a weighted
spring and a dashpot, while the second is an
RLC circuit.

A Weight, a Spring, and a Dashpot

The
system we are modelling consists of a weight,
one side of which goes through a spring to an
inertial reference (ground), with the other
side of the weight going through a dashpot to
ground. (Because we are here on earth, the
weight is supported by frictionless wheels so
that we needn't consider the effects of
gravity.) A "dashpot" is a disc or paddle
submerged in oil; it is used to "damp" or
lower the Q of the system. A force from the
outside (an input signal) is then imposed on
the above system, with the weight's behavior
being observed. (The weight's displacement,
velocity, and acceleration correlate directly
with the low-pass, band-pass, and high-pass
functions, respectively.)

First, we must derive a mathematical model
of the above mechanical system so that we can
build its "analog" electronically. The basic

equation can be gotten by equating forces--
the forces being mass times acceleration, the
oil's viscosity coefficient times velocity,
the spring constant times the displacement,
all balanced against the force imposed from
the outside.

We will call the input signal F(t) [read F
of t], a force as a function of time. M is
the mass of the weight, B is the viscosity
coefficient of the oil, and K is the spring
constant. Displacement of the weight will be
denoted X. Students of physics will recall
that acceleration is the 2nd derivative of X
with respect to time, while the velocity is
the lst derivative of X with respect to time.

The basic mathematical expression for the
system is:

F(t)=M(d²X/dt²)+B(dX/dt)+KX

Our next step is to build one, not with
rubber bands, a toy truck, and a spoon dipped
in cooking oil, but with our electronic
Tinker Toys of operational amplifiers. As
customary, we will use two integrators and a
summing amplifier as the main components of
our system. As students of Al Alden's series
on Op-Amps, you will recall that integrators
are op-amps with capacitors as their feedback
element (see Part III), and that a summing
amplifier (one with multiple inputs) is
gotten simply by adding more input resistors
onto an inverting amplifier.

We will make the following compromises to
enhance the intuitive understanding of the
analog simulation: (l) We will ignore the
fact that all of the op-amps invert
(attaching the negative sign) the signal as
they perform their function; we will put
necessary inversions in black boxes outside
the main elements where we can see them.
(2) The gains of the main building blocks--
the integrators and the summers--are taken as
one. Often, coefficients of the X terms in
the equation are included as gains in the
main building blocks; we will bring these out
separately where we can see them.

Since we are using integrators to solve the
basic equation, we could rewrite the equation
in terms of its integrals. This is more
cumbersome and, as it turns out, we don't
have to do so if we are willing to traverse
our integrators backwards. For example, an
integrator whose output is X as a function of
time has the first derivative of X with
respect to time on its input. When we create
our analog simulation, we will draw the
integrators so that their outputs point to
the left.

The building blocks and their positions
will be easier to imagine if we rewrite the
equation as follows:

M(d²X/dt²)=F(t)-B(dX/dt)-KX

Dividing both sides by M, we have:

D²X/dt²=(1/M)[F(t)-B(dX/dt)-KX]

Analog Simulation Circuit

Two integrators,
their outputs pointing to the left, are connected in cascade. The output of the leftmost one, A1, gives us the displacement X,
while its input is the velocity, the lst derivative of X with respect to time. This
input is being fed by another integrator, A₂,
whose input becomes the acceleration, the 2nd
derivative.

Below this cascade of integrators is a
summing amplifier which has three inputs.
One of the three is the input to the system,
F(t). Another is being fed from a -K black
box, with the input of this -K unit going
back to X, the output of A₁. Another input
to the summer is from a -B black box, with
the input of this block being gotten from
between the integrators, the lst derivative.
The output of the summer goes through a black
box of 1/M, the output of this latter unit
going to the input of A₂, the 2nd derivative.

The input of A₂, the 2nd derivative, is the
high-pass output. Between the integrators,
the lst derivative, is the band-pass output.
The output of A₁, the displacement X, is the
low-pass output.

In the above, the input of A₂, the 2nd
derivative, gets the sum of terms in the
right half of our equation, all passed
through a 1/M black box. As mentioned
earlier, efficient analog simulation would
have the scaling elements such as 1/M,
B, and K incorporated into the gains of the
various stages. Also, since all the stages
are inverters, minus signs in the black boxes
need not be included.

Intuitive Explanation

In the spring, mass
dashpot system with a sinusoidal force applied as an input, the displacement velocity
and acceleration of the mass correspond to
the low-pass, band-pass, and high-pass outputs of the filter.

If we apply a low-frequency signal to the
system, the displacement is proportional to
the force. This is true up to frequencies
where the inertial force of the mass (its
mechanical impedance) becomes equal to the
stiffness force of the spring. This is the

critical frequency. For higher frequencies,
the displacement decreases as the input frequency increases; i.e., a low-pass "filter."

At high frequencies where the inertia of
the mass is predominant, the acceleration is
proportional to the input force. As the
frequency drops below the critical frequency,
the acceleration decreases; i.e., a high-pass
filter.

At the critical frequency, the velocity of
the mass reaches a peak and decreases for
both higher and lower frequencies; i.e., a
band-pass filter.

In the low-frequency range, the performance
of a system of this type is characterized as
being spring- or stiffness-controlled, the
high-frequency performance as being mass- or
inertia-controlled, and the mid-frequency
(near the critical frequency) as being
resistance- or viscosity-controlled.

The Q of the System

With a given mass and
a given spring constant, the Q can be varied
by changing the viscosity of the oil; in
fact, the Q and the damping factor B are
inversely proportional.

Q = ω_criticalM/B

(or Q equals the product of the angular frequency times M, divided by B)

(ω_critical (or lowercase omega_critical) is the angular frequency and
is 2 times pi times the frequency in Hertz.)

ω_critical = √(K/M)

(or the angular frequency equals the square root of the quotient of K divided by M)

In some analog simulations, the damping
factor B is accomplished by putting a damping
resistor (one of very high value) across the
feedback capacitor in the A₁ integrator.

Series RLC Simulation

On the advice of the
good Mr. Alden, this analagous problem has
been included. A voltage of V(t) has across
it the series combination of an inductor, a
capacitor, and a resistor. Kirkhoff's Law
tells us that we can equate voltages around
the circuit.

V(t)=L(dI/dt)+(1/C)∫V_Cdt+RI

(or V as a function of time equals the product of L times the quotient of dI divided by dt, that product plus the reciprocal of C times the integral of V_Cdt, that product plus RI)

Rather than solve the RLC problem in this
form, we can make the problem look exactly
like our other one by rewriting the equation
in terms of the flow of charge q. Three bits
of trivia are necessary tools to get us
there:

1. I=dq/dt with respect to time.
2. V_L=L(dI/dt); this now becomes V_L = L(d²q/dt²).
3. The voltage across the capacitor
   will be q/C.

We can now write the basic equation:

V(t)=L(d²q/dt²)+R(dq/dt)+(1/C)q

Solving for the 2nd derivative as we did before:

d²q/dt²=(1/L)[V(t)-R(dq/dt)-(1/C)q]

RLC Simulation Circuit

Two integrators in
cascade have their outputs pointing to the
left. The left-most one, A₁, has its output
labelled q, with its input being the lst
derivative of q. The input of the other
integrator, A₂, bears the label of the 2nd
derivative of q with respect to time.

Below these integrators is the summing
amplifier with the following three inputs:
(1) V(t), the input signal. (2) The q output
of A₁ through the black box, -1/C. (3) The
points between the integrators going through
the black box -R. The output of the summer
goes through a box labelled 1/L, its output
going into A₂.

The output of A₁, just plain q, is low
pass. From between the integrators we get
the first derivative of q, the band-pass
output. The input of A₂, the 2nd derivative
of q, is the high-pass output.

The Q of the System

With a given L and C,
the damping factor which determines Q is R; R
and Q are inversely proportional.

Q= ω_criticalL/R

(or Q equals the product of angular frequency times L, divided by R)

ω_critical (or lowercase omega _critical) is the angular frequency and
is equal to 2 times pi times the critical frequency in Hertz.)

ω_critical =1/√LC

(or lowercase omega_critical equals 1 divided by the square root of the product of L times C)

The above systems are tunable, if you don't
mind varying all the coefficients at once
(quite a tracking problem). Wouldn't it be
just dreamy if we found a way to gang all of
these gain adjustments together? This brings
us to the next section.

Part II
The "Switched Capacitor" Technique

The 2nd-order analog simulation within the
5620 filter chip is done entirely without
resistors. Resistors are "simulated" by
switching capacitors (at a very high sampling
rate) between two voltages. The resultant
"equivalent" resistors are frequency-
dependent; their value changes in accordance
with the clock signal controlling the
switches. Let us by example make such a
resistor out of a capacitor and a high-speed
switch.

A clock-driven, single-pole double-throw
switch has its arm going through a capacitor
to ground. A voltage V₁ is on position 1,
while another voltage V₂ is on position 2.
The charge that flows from V₁ to V₂ is C
times the difference, V₁ - V₂. If the
switch is operated fast enough, an average
current equal to the 1st derivative of q will
flow:

I_average=C(V₁-V₂)f_clock

(V₁-V₂)/I is a resistor:

R_equivalent= 1/Cf_clock

The above gimmicks only replace resistors
in the filter system; feedback capacitors on
the integrators are not twitched or tampered
with. A couple of sample circuits for the
main building blocks of analog computation
are shown below:

Integrator

An op-amp has a feedback
capacitor from output to inverting input.
Instead of a resistor from the inverting
input to the input signal, the inverting
input goes to position 2 of an SPDT switch.
Input to the integrator is applied at position l. The swinger of the switch goes
through a capacitor to ground.

Summing Junction

A two-input version is
fairly easy to visualize. Two switches are
used. Position 2 of the first one goes to
the inverting input of an op-amp (this could
be a summing amplifier or even an integrator); position 1 becomes one of the inputs of
the summer. The arm of this first switch
goes through a capacitor to the arm of the
second switch. Position l of the latter is
grounded, while position 2 is the second
input to the summer. Inversion of the second
input signal is accomplished.

Actual Switching Arrangement

MOS/FET's
(single-pole single-throw switches) are
actually used. The gates of these MOS/FET's
are operated by a flip-flop; the gate of one
goes to the Q output of the flip-flop, while
the gate of the other goes to the flip-flop's
Q bar output. In this way, the SPST switches
are closed alternately. The drain of one
goes to the source of the other, and this
common connection becomes the "swinger" of
the equivalent SPDT switch.

As stated in the literature, the "resistors" have a delay equal to one cycle of the
controlling flip-flop (this is twice the
period and half the frequency of the clock).
Delay problems are offset by trading positions of the FET gate leads on adjacent
stages; the switches of adjacent stages are
out of phase with each other. It is important to note that the main component of high-
frequency noise introduced by the switched
capacitor technique will be at the "sampling
rate frequency," one-half the clock frequency. This noise will be farthest away
from the audio spectrum when a high ratio of
clock-to-filter frequency is chosen. However, if the filter is to be used at high
frequencies, limitations of the op-amps dictate that lower clock-to-critical frequency
ratios must be used.

In the literature, they do not show an
equivalent circuit for the analog simulation
which would explain the fact that the filter
has multiple inputs and one output, as
opposed to having one input and three outputs
(see our simulation in Part I). Derivation
of this analog simulation is left up to the
reader--anybody else but me.

Using the R5620 Filter Chip

"Good Gravy, do I have to know all that!?"
No, and a skeletal description of the chip
will do much to point the way to hooking it
up.

Description

The R5620 is an l8-pin DIP
package. Three of these are supply pins
(ground, along with plus and minus voltages).
The frequency-determining scheme, the Q
selection scheme, and the audio input and
output connections are discussed below:

1. The chip has a clock input pin into
   which a high-frequency pulse is fed. Two
   clock circuits will be discussed later, one
   using a 555 timer and a crystal oscillator
   using CMOS inverters. A 5-bit binary number
   imposed on 5 input pins selects the ratio of
   clock to F₀. Counting down from 11111 to
   00000 brings this ratio up logarithmically
   (in steps of about 3 percent) from 50 to 200.
2. The Q is selected by choosing a 5-bit
   binary number to be imposed on another set of
   5 pins. The range of available Q's is from
   0.57 to l50, as you count up from 00000 to
   11111.
3. The filter has one output pin from
   which the filtered audio signal is taken.
   Three input pins are provided for the three
   functions, low pass, high pass, and band
   pass. Being a 2nd-order filter, the roll-off
   for the low- and high-pass sections is l2dB
   per octave; the band-pass roll-off approaches
   6dB per octave for frequencies either side of
   F₀.

Basic Hook-up

Pin 8 goes to ground, pin l
goes to the minus supply, and pin ll goes to
the plus supply. A signal from a clock
oscillator goes to pin 7.

Pins l3 through l7 accept the binary code
for setting the frequency divider (pin l7 is
the least significant bit, and pin l3 is the
most significant bit). The number 00000
causes the chip to divide the clock frequency
by 200; 11111 divides it by 50.

Counting downward from pin 6 through pin 2
(pin 2 being the least significant bit, and
pin 6 being the most significant), we have
the 5 pins which accept the Q-determining 5-
bit code. An address code of 00000 sets Q at
0.57; 11111 sets it for its maximum, l50.

One can either hard-wire these inputs to
their respective logic levels, or use

switches to make them selectable from the
front panel. By connecting each pin through
a pull-up resistor to logic 1 (or a pull-down
resistor to logic 0), one can then use SPST
switches to pull them in the other direction
(to 0 if pull-up resistors are used, or to 1
if pull-down resistors are used). One nifty scheme would be to use a hexadecimal switch
(a l6-position switch whose output is a 4-bit
binary number) to control the 4 least significant bits; then a toggle switch could be
added to control the most significant bits,
sort of a "range" switch. With this arrangement, you can dial in any number you like.*

Selection of low-, high-, and band-pass
functions is done by grounding the unused
inputs and feeding the signal into the
desired one. A notch filter can be gotten by
tying the low- and high-pass inputs together
--of course, grounding the band-pass input.

In all cases, unused inputs should be
committed somewhere, and/or protected by
resistors where appropriate. The binary
inputs should be committed to ground or
either supply line at all times. Any signal
from the outside world (not from previous
stages in the project) should be connected to
its input through a resistor (4.7K or higher).

If you are tampering with any inputs on a
protoboard, commit these pins to some
reference with resistors before you disconnect and reconnect them. Failure to follow
these suggestions will cost you; I have
burned out several units with my blase
attitude.

Clock Circuits

The following two clock
oscillator circuits were provided courtesy of
Jules Madey, owner of Applied Inventions and
supplier of these chips. The filter chip
will tolerate these circuits being referenced
either to ground or to -V. This is nice to
know, since CMOS chips will not tolerate
voltages higher than l8 volts, whereas the
filter chip can be operated at 22 volts (+
and - 11 volts).

The first is a 555 timer set up to work
around 100kHz. Pin l goes to ground or to
-V, as the case may be. Pins 4 and 8 go to
+V. Pins 2 and 6 are tied together and go
through 680pF to pin l. Pins 2 and 6 also go
through 7.5K, then through a 5K rheostat to
plus V. Between pins 6 and 7 is 5.6K. The

output, pin 3, goes to pin 7 on the 5620.
(If a CMOS 555 is not used, there should be
0.luF connected between pins l and 8.)

A l MHz crystal oscillator is shown using
CD4049 inverters. The output of the first
goes through 680pF to the input of the
second. A l MHz crystal goes from the output
of the second to the input of the first.
Across each inverter (from its output to its
input) is a high-value resistor (l0 or 20
megOhms). The output of the second goes
through another section (through another
inverter) which serves as a buffer.

The above crystal oscillator can be fed
into a CD4520 counter (a chip containing 2
sets of 4 flip-flops in cascade). In this
way, you can also get crystal-controlled
frequencies of 500, 250, l25, and 62.5kHz.
Pin 8 of the 4520 goes to -V (or to ground),
while pin l6 goes to +V. One section of this
chip is disabled by connecting pins 9, l0,
and l5 to pin 8. Pin l, the clock input,
goes to the output of the crystal oscillator.
Pin 2, the enable, goes to +V. Pin 7, the
reset, is tied low (tied to pin 8). The
outputs, in order of descending frequency,
are pins 3, 4, 5, and 6.

Sample Circuit
(Very Sample)

Suppose we want a low-pass filter with a
"maximally flat" response and a cut-off
frequency of 7.5kHz. First, let us pick a
divisor and a clock frequency suitable for
this F₀--say a ratio of 50 (a binary number
of 11111), thus a clock frequency of 375kHz.
Second, the Q desirable for a maximally flat
response is 0.707, a binary input of 00010.
The circuit follows:

Pin l goes to -V, pin ll goes to +V, and
pin 8 is grounded. The unused inputs, pins 9
and l8 (band-pass and high-pass, respectively), are grounded. Pin l0, the low-pass
input, goes through 47K to the signal source.
Pin l2 is the output. (Load capacitance
should not exceed 50pF; otherwise, feed pin
l2 through a resistor of perhaps l0K to the
load.)

Pin 7 goes to a clock of 375kHz. Pins l3
through l7 go to +V. For our Q selection,
pins 2, 4, 5, and 6 can go either to ground
or to -V. Pin 3 goes to +V.

Notes on Q

For the band-pass and notch filter, Q is
expressed in terms of bandwidth: Q equals
the critical frequency divided by the bandwidth.

For the band-pass filter, the critical
frequency will be at the peak of the response
curve. The bandwidth is the difference in
frequency between the upper -3dB frequency
and the lower -3dB frequency. For example,
if a band-pass filter is tuned for maximum
output at l000Hz, and the -3dB points are
found to be 1050Hz and 950Hz, the bandwidth
is 100Hz; the Q will be 1000 over 100, or a Q
of 10. If we know the Q to be 20, the bandwidth will be 1000 over 20, equals 50Hz; the
-3dB points will be at 975Hz and 1025Hz.

This relationship holds true for the notch
filter as well. In this case, the bandwidth
is the difference in frequencies between the
-3dB points at which the signal falls off as
you approach the notch (not the points 3dB up
in response from the bottom of the notch).

For high- and low-pass filters, the response will be "maximally flat" at Q equals
0.707 (an address code of 00010). The
response will become "peaky" at Q's higher
than this; a hump will develop before cut-off
is reached. In fact, the gain of the filter
at the critical frequency will be equal to Q.
Therefore, you can see that with a Q of 10
(thus a boost in response of 10 times the
gain at other desired frequencies) the filter
will have what would usually constitute an
undesirable effect on the signal. (Actually,
the peak of this hump will be offset slightly
from F₀, and so there will be a point in our
above example in which the boost in gain is
greater than 10 times.)

Specifications

Supply Requirements

A split supply is needed; from + and - 4V
to + and - 11V. Powered from + and - 10V,
the current drain is 4.5mA, typical. Being
CMOS and given this low-current drain, a
single supply can be used if a suitably husky
voltage divider is put across the single
supply, the junction of the divider going to
the filter's ground pin. (Jules Madey of
Applied Invention recommends using two 220
ohm resistors for supplies of 8 to 15 volts.)

Clock Input:

Logic low--0.8V (above ground) or lower,
not to go more than 0.5V below VSS.

Logic high--2V (above ground) or higher,
not to exceed VDD.

Minimum trigger pulse width--200 nanoseconds

Range of acceptable clock frequencies--10Hz
to 1.15MHz, can be extended to 2MHz for low
values of Q.

Clock input capacitance--10pF maximum

Data Inputs (Both Q and Frequency Selection):

Logic low--0.4V (above ground) or lower,
not to go beyond 0.5V below VSS.

Logic high--2V (above ground) or higher,
not to exceed VDD.

(These are very high impedance inputs and
are subject to damage when moving them from
one logic level to another on a protoboard.
I recommend committing them somewhere with
resistors of perhaps 47K.)

Audio Filter Specs:

(These figures are given for a supply of
+ and - 10V, 20V total. Note that the noise
and dynamic range figures are for very large
signals, taking advantage of the filter's
full output swing.)

Range of acceptable F₀--0.05Hz to 25kHz.

Insertion loss--0dB.

Output swing--14V peak-to-peak (for Q
equals 1).

Output noise--270uV (for Q equals 1; noise
is broadband up to 1/4 of the clock frequency).

Dynamic range--94dB (for Q equals 1), 84dB
(for Q equals 40).

Total harmonic distortion--0.2% (for 14V
peak-to-peak swing).

Input impedance--1 megOhm, minimum.

Input capacitance--20pF, maximum.

Dynamic output impedance--10 ohms, typical.

Maximum load capacitance--50pF.

Maximum output load current--4mA.

Table I
Q Selection

Listed below are the binary input codes,
followed by their respective Q. While the
manufacturer says that these Q values will
typically be within 5% of those given, they
only guarantee that the actual Q will be 2/3
of those values given. Gee, thanks.

• 00000--0.57
• 00001--0.65
• 00010--0.71
• 00011--0.79
• 00100--0.87
• 00101--0.95
• 00110--1.05
• 00111--1.20
• 01000--1.35
• 01001--1.65
• 01010--1.95
• 01011--2.2
• 01100--2.5
• 01101--3.0
• 01110--3.5
• 01111--4.25
• 10000--5.0
• 10001--5.8
• 10010--7.2
• 10011--8.7
• 10100--10.0
• 10101--11.5
• 10110--13
• 10111--15
• 11000--17.5
• 11001--19
• 11010--23
• 11011--28
• 11100--35
• 11101--40
• 11110--80
• 11111--150

Table II
Programmable Frequency Divider

Listed below are the binary codes followed
by their respective frequency divisor, the
clock frequency over F₀. As stated in the
literature, you can pick a number which will
get you within 3% of a desired critical frequency (the actual ratio from one to another
is the 31st root of 4). The ratio of clock
to critical frequency should be kept high at
lower F₀'s to avoid the switching noise
(which becomes more significant above 1/4 the
clock frequency). For high filter frequencies, however, this ratio will have to be
lower because of limitations of the op-amps
(they don't say what will be the evidence of
these limitations).

• 00000--200
• 00001--l9l.3
• 000l0--l82.9
• 000ll--l74.9
• 00l00--l67.2
• 00l0l--l59.9
• 00ll0--l52.9
• 00lll--l46.2
• 0l000--l39.8
• 0l00l--l33.7
• 0l0l0--l27.9
• 0l0ll--l22.3
• 0ll00--ll6.9
• 0ll0l--lll.8
• 0lll0--l06.9
• 0llll--l02.3
• l0000--97.8
• l000l--93.5
• l00l0--89.4
• l00ll--85.5
• l0l00--8l.8
• l0l0l--78.2
• l0ll0--74.8
• l0lll--7l.5
• ll000--68.4
• ll00l--65.4
• ll0l0--62.5
• ll0ll--59.8
• lll00--57.2
• lll0l--54.8
• llll0--52.3
• lllll--50

Table III
Pin Connections, R5620

• Pin l--VSS (minus supply)
• Pin 8--ground (common connection of the
  two supplies)
• Pin ll--VDD (plus supply)
• Pins 2 through 6--programmable Q
  selection (pin 2 is the least
  significant bit)
• Pins l3 through l7--programmable
  frequency ratio (pin l7 is the
  least significant bit)
• Pin 7--clock input
• Pin 9--band-pass input
• Pin l0--low-pass input
• Pin l8--high-pass input
• Pin l2--output

*Addresses and Miscellaneous

For having gobs of fun selecting frequency
ratios and Q's, hexadecimal switches can be
used. These have l6 positions and generate a
4-bit binary number (a common terminal or arm
is tied to a logic level). One such switch
could be assigned to the four least significant bits on a set of inputs, while a toggle
switch could be used to control the 5th bit.
The arms of the switches can go to ground or
to VSS when used with this filter chip.

Jameco Electronics, l355 Shoreway Rd.,
Belmont, CA 94002, phone (4l5) 592-8097,
sells a thumb-well hex switch, catalog No.
SF-53. In addition to the switch unit, "end
plates" are required for mounting, SF-EP
(come by the pair). You can stack up as many
switches as you wish by using the end plates
on either side of the stack and by putting
"divider plates" between them (SF-DP).

The R5620 and other Reticon items are
available from Applied Invention, R.D. 2,
Route 2l, Hillsdale, NY l2529, phone (5l8)
325-39ll. The man who owns this company is
Mr. Jules Madey; he was for many years the
Chief Engineer on the staff of Smith-
Kettlewell. Mention my name and you're "in
like Flynn."

A TUNABLE AUDIO NOTCH FILTER
USING THE RETICON R5620

The original name for this article was
going to be "A Tunable Notch Filter for the
Short Wave Listener." What elusive things
are electronics projects--everything works on
the bench and you proudly bring your SWL
receiver into the shop hoping to hear Radio
Nederlands without a piercing 5kHz interference tone. Your elation is short-lived as
you turn on your filter only to find the
harmonics of your clock signal put Radio
Nederlands to shame as far as signal strength
is concerned. Well--hmmm--you could do
wonders for a tape of Radio Nederlands. I
was able to turn this filter into a PA system
on which I could notch out the dominant feedback frequency, and thus I could sing louder.

I am not ready to give up on the idea of a
short wave filter, especially where a receiver with good shielding and an antenna
with a shielded lead-in is used. The next
obvious thing to try will be to enclose the
filter circuit in a grounded metal box,
enclosing an RF filter to "bottle up" the
clock signal. The unit described illustrates
what will be my first attempt along these
lines.

The filter uses a Reticon R5620 programmable filter in the "notch" configuration
(low-pass and high-pass inputs tied
together). I chose to include an audio
amplifier and speaker as part of my project.
The filter could be built with the intention
of feeding it into another amplifier and
speaker system, provided the constraints on
the filter's output circuit are observed
(load capacitance must be under 50pF, and
peak output current should not exceed 4mA).

The filter is driven by a tunable clock
using a 555 timer (trying a CMOS 555 did not
reduce RF interference from the clock). The
clock is tunable over a range of 5 to 1. The
5 address lines of the frequency divider in
the filter chip are all tied together and go
to a toggle switch so as to give the user two
ranges--one is 4 times the frequency of the
other. In other words, one range will fall

from l to 5kHz, while the other will cover
from 250Hz to l2,500Hz.

A 3-position "Q" switch permits the user to
select a Q which suits his purpose. My
primitive Q-selection scheme is done more out
of convenience than for the reasons of good

science. Three independent toggle switches
could be used to give the user more combinations of the Q inputs.

Background noise from the filter is evident
with the gains chosen. The ambitious builder
might consider preceding the filter chip with
a preamplifier (an op-amp with a gain of
perhaps 5), then reducing the gain into the
audio output stage by increasing its 47K
input resistor to perhaps 220K. This would
better exploit the full dynamic range of the
filter chip and put the signal well above the
noise. However, as it stands now, the filter
is much less noisy than the signals I was
interested in processing with it.

As required by the filter chip, a split
supply (plus and minus voltages about ground)
must be used. I used two groups of 4 penlight cells to get plus and minus 6 volts.
The audio amplifier, on the other hand,
operates across the entire supply of l2
volts. Just to keep all input and output
commons the same, I used the minus 6V line
as signal ground.

Circuit

Two 6V batteries are connected in
series, with their common connection going to
the 5620 filter's ground pin, pin 8. Pin 9
of the filter, the unused bandpass input, is
also tied to pin 8. A double-pole, single-
throw switch must be used to turn the filter
on and off. The positive side of the plus 6V
battery goes through one pole to the plus 6V
line, while the negative side of the minus 6V
battery goes through the other pole on the
switch to the minus 6V line. Pin l of the
filter goes to the minus 6V line, while pin
ll goes to the plus 6V line.

Pin l of a 555 goes to minus 6V, while pins
4 and 8 are tied together and go to plus 6V.
A disc capacitor of 0.luF is connected
between pins l and 8. Pins 2 and 6 are tied
together and go through 0.00luF (mica) to the
minus 6V line. Pins 2 and 6 also go through
l.8K, then through a l0K rheostat to the
output, pin 3. (This crazy scheme of driving
a 555 with its own output gives nice broad
pulses with which to clock the filter, as
well as allowing for considerable range.)

Pin 3 of the 555, the clock output, goes to
the clock input of the filter chip, pin 7 of
the 5620. Pins l3 through l7 are tied together (these are the programmable frequency
divider inputs) and go through 47K to the
minus 6V line. These pins also go through a
single-pole, single-throw toggle switch to
the plus 6V line. (With the switch open, the
divisor is 200; with the switch closed, the
divisor is 50.)

The least significant bits of the Q selection pins, pins 2 and 3, are tied together and go to minus 6V. Of these address lines,

pins 4, 5, and 6 each go through 47K to the
minus 6V line. Pins 4, 5, and 6 go to positions l, 2, and 3, respectively, on a 3-
position Q selector switch; the arm of this
switch goes to the plus 6V line. (This gives
us Q's of 0.87, l.35, and 5.0, in accordance
with the binary numbers 00l00, 0l000, and
l0000, respectively.)

The sleeve of the audio input jack is
common to the metal cabinet housing the
filter. This cold audio lead also goes
through an RF choke (2.5mH) to the minus 6V

line. The tip of the jack goes through
another RF choke (2.5mH), then through 0.luF,
then through 47K to both pins l0 and l8 of
the filter which are tied together (these are
low-pass and high-pass inputs, respectively).
The input jack is shunted by 0.0luF; between
the far ends of the RF choke is connected
another 0.0luF capacitor.

The output of the filter, pin l2, goes
through 47K, then through l0K to the minus 6V
line (this l0K resistor could very well be a
volume control). The junction of these
resistors (or the arm of the volume control)
goes through 0.luF to pin 3 of an LM386.
Pins 2 and 4 of the 386 go to the minus 6V
line. Pin 6 goes through l0 ohms to the plus
6V line; pin 6 also goes through 250uF to
minus 6V (negative at the minus 6V line).
Pin 7 goes through 25uF to minus 6V (negative
at the minus 6V line). Between pins 4 and 5
of the 386 is connected 0.22uF.

Pin 5, the output of the 386, goes to the
positive side of a l00uF capacitor, with its
negative end going through a speaker to the
minus 6V line. If an earphone jack is to be
included, the output leads must also be
isolated for RF. The aforementioned 2.5mH RF
chokes will have too much resistance to permit duplicating this filter on the output.
However, output leads from the board can be
twisted together in a "twisted pair," after
which these leads should be wrapped around a
hunk of ferrite (preferably wrapped in a
toroid through a ferrite toroidal coil form).

Parts List

Resistors:

• l--l0 ohms
• l--l.8K
• l--l0K (or l0K volume control)
• 6--47K
• l--l0K rheostat

Capacitors:

• l--0.00luF mica
• 2--0.0luF disc
• 3--0.luF disc
• l--0.22uF disc
• l--25uF electrolytic, l2V
• l--l00uF electrolytic, l2V
• l--250uF electrolytic, l2V

Switches:

• l--DPST toggle (on-off)
• l--SPST toggle (frequency range)
• l--Single-pole, 3-position rotary(Q selector)

Semiconductors:

• l--NE555 timer
• l--LM386 audio amplifier
• l--Reticon R5620 filter
  (Available from Applied Invention,
  R.D. 2, Route 2l, Hillsdale, NY
  l2529; phone 5l8-325-39ll)

THE SMITH-KETTLEWELL
TRAINING AID FOR PIANO TUNERS

Abstract

This is primarily a tool to
facilitate training of prospective tuners;
however, its small size permits its being
included in the tuning kit of veterans. The
aid is an electronic filter which emphasizes
the subtle beating of the harmonics of a pair
of notes (4th and 5th intervals) which are
played together in laying the temperament
octave. It is not an "electronic tuning aid"
(strobe tuner), the use of which is controversial in the piano tuning industry.
Rather, it is designed to remove the subtlety
of the sound of beats from intervals as they
are tuned in the regular way. For those not
in the piano business, this project contains
a couple of circuits of interest; it well
illustrates a use for the Reticon R5620
filter chip, and it contains an elemental PLL
frequency synthesizer.

Introduction

The easy part in tuning a piano is matching
up high and low notes of the keyboard to a
previously tuned "temperament octave" in the
middle register. The task which apprentices
find hard to learn and for which even old
salts must stay in practice is laying the
temperament octave. As was discussed in
"Singing Chips," Winter l982, the equally
tempered scale is not based on ratios of
whole numbers. Except for octaves, which are
perfect, compromises are made throughout the
temperament; intervals which are nearly whole
number ratios are tuned slightly off in order
to create equally spaced ratios within the l2
tones as we know them.

Purposefully creating the above imperfections within the temperament octave requires
listening to subtle "beats" in the interval's
"4th's" and "5th's." The "beats" of interest
are not simply the difference frequency
between two notes. The tuner is listening
for the near coincidence of harmonics of each
note; for example, the second harmonic of
middle C and the third harmonic of the F
below it both land on C above middle C. It

is academic to say that these two notes
should be tuned so as to beat once every l.7
seconds--it is quite another matter to pull
this information out of all that noise. The
notes themselves are louder than the harmonics you are listening for, the harmonics
are not of equal intensity and no perfect
cancellations occur, and higher harmonics are
always there to confuse the issue.
For training purposes, and perhaps on the
job, a simple bandpass filter can sector out
the "beep note" of interest so as to make it
more audible. The Reticon R5620 is a filter
which can be easily tuned to the desired beat
note frequencies. [Tim Cranmer tells me that
Helmholtz tried this scheme using tuned
cavities (Helmholtz resonators), one for each
interval. These and other tidbits can be
found in his arduous work, "The Sensations of
Tone."]

Design Considerations

One could make a very simple version of
this device by driving the Reticon filter
with a tunable clock; the user would adjust

the filter to the desired harmonic every time
an interval was to be tuned. I wanted the
frequencies to be available on a selector
switch, both for convenience and to afford
rapid comparisons between adjacent intervals.
What an engineering bonus it would be if the
filter's programmable divider moved in steps
of the equally tempered scale (the l2th root
of 2 instead of the 3lst root of 4). Alas,
this is not the case, and it was necessary to
build a frequency synthesizer which follows
the traditions of the equally tempered scale.

A "musical clock" for the filter was made

using an MK50240N top-octave generator (organ
chip) was used in conjunction with a CD4046
phase lock loop IC to make an equally
tempered frequency synthesizer. This whole
PLL system is then driven by a low frequency
clock which need be adjusted only once.
Because tuners sometimes wish to tune the
piano at other than standard pitch (if a
clunker is old enough, it won't stand the
strain), the main low-frequency clock is
variable over a small range.

A "Q" of about l7 was chosen experimentally; it was sufficient for attenuating the
unwanted signals, yet leaving adjustment of
the filter non-critical. The rest of the
design was very straightforward; a microphone
preamp picks up the signal through an electret condenser microphone in the tuning aid
box, whereupon it is fed through the filter
to an LM386 audio amplifier which drives an
earphone.

Synthesizer

A PLL was set up with its main
input signal being a low-frequency oscillator
tunable over a small range (using a 555).
Between the PLL's VCO and the VCO phase
detector input is inserted a frequency
divider--in this case, the frequency divider
is selectable and is one of the set within
the 50240 organ chip. In other words, the
PLL VCO output goes to the clock terminal of
the organ chip, and a desired output from the
organ chip goes to the phase detector (pin 3
of the CD4046). On the other phase detector
input (pin l4 of the 4046) is a main clock of
437.9Hz (this is not a musical pitch, as you
will soon see).

Selection of the various outputs (divisors)
on the organ chip causes the PLL VCO to run
at an appropriate multiple which puts the two
phase detector inputs in synch. Whichever
output of the top-octave chip is chosen, it
will be driven so as to duplicate the 437.9Hz
tone of the main clock. The organ chip's
clock input will be driven in accordance with
the equally tempered scale as these outputs
are presented to the phase detector.

As per the table of divisors in "Singing
Chips," the smallest divisor on the 50240 is
239. Therefore, the PLL VCO will be running
at a high frequency. It makes sense, then,
to set the filter's programmable divider to a
high value, 200 being convenient. The lowest
"f0" (filter's critical frequency) we will
need for tuning the temperament is C above
middle C, 523.3Hz. The filter must be
clocked at 200 times this frequency,
l04.66kHz. After this, the frequency of the
main clock into the PLL system can be found
by dividing l04.66 by 239, 437.9Hz.

The Q of our filter is loose enough, however, to permit this 437.9Hz tone to be used
as a reference pitch; the filter can be tuned
by matching this clock frequency to 440Hz. A
pushbutton is provided for this purpose.

Picking a higher divisor on the organ chip
will make the PLL VCO run faster. For example, the largest divisor on the organ chip
is 478; this would make the PLL VCO run at
209.32kHz, putting the f0 of the filter at
6th-octave C, l046.6Hz. Note that the outputs of the organ chip which before gave us
its low notes (large divisors) give us high
clock frequencies and high f0's; musically
speaking, the sequence of its pins are
reversed. A table of filtered "notes" versus

chip pins is given later in the discussion of
piano tuning.

I built my prototype in a bakelite box
measuring 2 by 3 by 6 inches. Though I would
sooner endure a flogging as do it the same
way twice, I built my circuit on a piece of
perforated Vector board measuring 3 inches
square. The size of my circuit board was
inappropriate, but my layout bears considering. The board, which should be perhaps 3 by 4-l/2 inches, can be divided lengthwise
by the supply lines (both plus and minus 6
volts are required). A bus line for ground
(the common connection between the two 6-volt
supplies) runs along the top edge. The board
then has a top and a bottom section separated
by the supply buses.

With the component side toward you and the
ground bus along the top edge, it makes sense
to use the top section for the audio circuitry and the bottom section for the synthesizer. From left to right in the top
section, first install the two-stage mike
preamp, then the filter, and finally the
LM386 audio output stage. Similarly across
the bottom it makes sense to put the PLL in
the middle, the organ chip to its left, with
the main clock being at the lower right.

The microphone, the earphone jack, the
volume and pitch controls, the on-off switch,
the l2-position synthesizer selector, and the
pitch reference pushbotton were all mounted
on the top panel of my bakelite box. The
Radio Shack microphone element is omnidirectional, so it does not appreciably
affect pickup if it is not aiming directly at
the piano. This mike element was cemented
into a 7/l6 inch hole.

Constraints on the battery supply are

rather severe; two packs of four AA cells
were used in series to get the plus and minus
6 volts about ground. I would have preferred
to use 9-volt batteries, but the organ chip
is constrained to work under l6 volts, and
the LM386 does not work on voltages much over
l2 volts.

"Synthesizer noise" proved to be quite a
problem; I never succeeded in eliminating it

from the LM386. No doubt this is partly due
to my poor choice of circuit boards, since
some of the parts are literally sitting on
top of each other. However, there are many
devices generating audio frequencies contained in this project, and a constant din of
organ noises and hum from the main clock can
be heard, even with the volume turned down.
Some reduction in noise from the main clock
was achieved by switching to a CMOS 555.
This device, along with the other specialty
item, the organ chip, can be gotten from
Jameco Electronics, l355 Shoreway Rd.,
Belmont, CA 94002; phone: (4l5) 592-8097.

[Since this paper was written, I was able
to reduce the noise by l5 or 20dB simply by
cabling (bundling together) the wires from
the selector switch--a remarkable effect. In
my original unit, I got further noise reduc
tion by connecting 500uF between the plus and
minus supply busses. Units built since then
have had the advantage of better layout, and
this capacitor proved to be unnecessary.]

Circuit

The positive side of the minus 6-
volt battery and the negative side of the
plus 6-volt battery are grounded. The minus
6-volt battery lead goes through one pole of
a double-pole, single-throw toggle switch to
the minus 6V line, while the plus 6-volt
battery lead goes through the other pole on
this on-off switch to the plus 6V line. The
plus 6V line is bypassed to ground by l00uF
(negative at ground); the minus 6V line is
bypassed to ground by l00uF (positive at
ground). A decoupling network for the electret microphone is included; the plus 6V line
goes through 330 ohms, then through l0uF to
ground (negative at ground). The junction of
this resistor and capacitor goes to the
supply lead of the microphone.

The cold microphone lead is grounded; the
center conductor of its shielded cable goes
through 0.luF (Mylar), then through l0K
(metal film) to pin 2 of an LM358 dual op-
amp. Pin 3, the non-inverting input of A1,
is grounded. Pin 2, the inverting input,
goes through 243K (metal film, value not
critical) to the output of A1, pin 1.

The non-inverting input of A2, pin 5, is
grounded. The inverting input, pin 6, goes
through l0K (carbon composition) to pin 1.
A 220K feedback resistor (carbon composition)
is connected from output to inverting input
on A2 (from 7 to 6). Pin 4 of this 358 goes
to minus 6V, while pin 8 goes to plus 6V.

Pin 7 of the 358, the output of the two-
stage mike preamp, goes directly to the
bandpass input, pin 9, of the Reticon R5620
filter chip. The high pass and low pass
inputs, pins l0 and l8, are grounded. Pin
l2, the output, goes through 47K to the top
of a l0K audio-taper volume control, with the
bottom of this control being grounded.

Pin 1 of the 5620 goes to minus 6V, pin 8
is grounded, and pin 11 goes to plus 6V.
Pins l3 through l7, the binary inputs to the
programmable counter, are tied low (this can
be either to minus 6V or to ground; I used
minus 6V). (An address of 00000 sets the
frequency divider to 200.) A number of 11000
is impressed on the Q-selection inputs
(giving us a Q of about l7); pins 5 and 6 go
to plus 6V, while pins 2, 3, and 4 can either
go to ground or to minus 6V (I used minus
6V).

The arm of the volume control goes through
0.luF to pin 3 of an LM386 audio amplifier.
Pins 2 and 4 go to minus 6V, while pin 6 goes
through l0 ohms to plus 6V. Pin 6 is bypassed to minus 6V by l00uF (negative at the
minus 6V line). A 0.22uF capacitor goes
between pins 4 and 5; pin 5, the output, goes
to the positive end of a 47uF capacitor, the
negative end of which goes through the earphone to minus 6V.

A 555 or CMOS ICM-7555 is used as the main
low-frequency clock. Pin l goes to minus 6V
while pins 4 and 8 are tied together and go
to plus 6V. A 0.luF capacitor goes between
pins l and 8 located close to the chip. Pins
2 and 6 are tied together and go through
0.luF (Mylar) to the minus 6V line. Pin 6
goes through l0K to pin 7, while pin 7 goes
through l0K, then through a 5K rheostat
(pitch control) to the plus 6V line. Pin 3,
the output, goes to pin l4 of the PLL.

To create a reference pitch for tuning the
filter, pin 3 of the 555 also goes through
1.5 megOhms to the arm of an SPDT pushbutton
switch. The normally open position of this
switch goes to the top of the volume control;
the normally closed contact goes to the
bottom of this control and to ground.

Pin 8 of the PLL (CD4046) goes to minus 6V,
while pin l6 goes to plus 6V. Located close
to the chip and connected between pins 8 and
l6 is 0.luF. The oscillator Enable, pin 5,
also goes to minus 6V.

As a loop filter, pin l3 (the output of the
wide-band phase detector) goes through 470K,
then through l20K, then through 0.47uF
(Mylar) to the minus 6V line. The junction
of the two resistors goes to pin 9, the VCO
input.

Pin 11 goes through 5.6K to the minus 6V
line. Between pins 6 and 7 is 0.00luF
(l000pF). Pin 4, the output of the VCO, goes
to the clock input (pin 2) of the 50240 organ
chip, as well as going to pin 7 (the clock
input) of the 5620 filter.

Pin l of the 50240 organ chip goes to the
plus 6V line, while pin 3 goes to the minus
6V line. Connected between pins l and 3 and
located next to the chip is 0.luF.

As mentioned, the pin l4 input of the phase
detector goes back to the main clock (the
555). The pin 3 input of the phase detector
goes to the arm of a l2-position, single-pole
switch. The various positions on this switch
go to outputs of the organ chip as follows
(the order in which they are connected
depends very much on the type of temperament
the tuner uses):

• Position l goes to pin l5.
• Position 2 goes to pin 8.
• Position 3 goes to pin l3.
• Position 4 goes to pin 6.
• Position 5 goes to pin ll.
• Position 6 goes to pin 4.
• Position 7 goes to pin l0.
• Position 8 goes to pin 5.
• Position 9 goes to pin l2.
• Position l0 goes to pin 7.
• Position ll goes to pin l4.
• Position l2 goes to pin 9.

The above system only allows tuning of
intervals within one octave in the middle
register. There are many tuners who would
choose to expand the range over which this
filter is usable. The general approach for
adding an octave switch is outlined below.

The filter can easily be raised an octave
by programming its frequency divider differently; an input address of 10000 changes the
filter's divisor from 200 to 97.8. Given our
chosen "Q," 97.8 can be considered l00 without retuning of the filter being necessary.

The simplest way of cutting the filter's
frequency in half is to insert a flip-flop
between pin 4 of the PLL and the filter's
clock input, pin 7. Other schemes, such as
dividing the low-frequency clock or tampering
with the PLL system in other ways, may necessitate readjustment of components of the loop
filter.

We leave it up to the ambitious builder to
design switching networks for these purposes.
Remember in changing the address lines, it is
perfectly acceptable to tie them low with
pull-down resistors and use a single-throw
switch to pull desired ones high.

By changing any of the components around
the 555, the placement of this filter in a
different range can be accomplished. The
frequency of the main clock can be calculated
by choosing the lowest harmonic involved in
your temperament, and multiplying this
frequency by 200/239. By trying different
timing capacitors on the 555, a new range for
the system can be chosen experimentally.

Besides depending on layout, interference
of synthesizer noise to the user will depend
heavily on the efficiency of the earphones.
If this noise is unbearable, try inserting a
resistor in series with the earphones; the
value of this resistor will have to be chosen
taking the impedance of the phone into
account--for 8-ohm phones, try l00 ohms.

Piano Tuning

There are many different schemes for tuning
a temperament; most primarily involve tuning
4th and 5th intervals alternately around one
octave. There are, however, even variations
within this scheme, and it will necessarily

be up to you to build the tuning aid to your
own specifications. It is hoped that the
three tables to follow can help you in doing
so. Following these, I will briefly describe
the temperament scheme which I learned from
my papa.

Table I
Synthesizer Connections

After each pin number of the organ chip is
listed the "note" of the filter's critical
frequency, followed by the interval for which
this frequency has been chosen. My temperament scheme includes the notes from 3rd
octave F through 4th octave E. These octave
signs will not be included in the table.
Note that the filter's critical frequencies

all fall within the 5th octave.

5ths:

• Pin l5--5th octave C, F to middle C
• Pin l4--5th octave C sharp, F sharp to
  C sharp
• Pin l3--5th octave D, G to D
• Pin l2--5th octave D sharp, G sharp to
  D sharp
• Pin ll--5th octave E, A to E

4ths:

• Pin l0--5th octave F, F to A sharp
• Pin 9--5th octave F sharp, F sharp to B
• Pin 8--5th octave G, G to middle C
• Pin 7--5th octave G sharp, G sharp to
  C sharp
• Pin 6--5th octave A, A to D
• Pin 5--5th octave A sharp, A sharp to
  D sharp
• Pin 4--5th octave B, B to E
• Pin l6--6th octave C; though not used in my
  temperament, this will work for
  middle C to F

Table II
Beat Rates

Within the range of 3rd octave F to 4th
octave E, the beat rates for 5th and 4th
intervals are listed. Two ways of expressing
these beat rates are given; the first is
generated by an Al-Alden computer program,
with the second being approximate "seat of
the pants" figures gotten from handbooks of
the l920's.

5ths (these are "contracted intervals"; they
are tuned so as to be narrower than perfect):

• F to middle C--0.59, once in l-7/l0
  seconds
• F sharp to C sharp--0.63, once in l-6/l0
  seconds
• G to D--0.66, once in l-5/l0 seconds
• G sharp to D sharp--0.70, once in l-3/7
  seconds
• A to E--0.74, once in l-l/3 seconds

4ths (these are "expanded intervals"; they
are tuned so as to be wider than perfect):

• F to A sharp--0.79, once in l-l/4
  seconds
• F sharp to B--0.84, once in l-l/5
  seconds
• G to C--0.89, once in l-l/8 seconds
• G sharp to C sharp--0.94, once in l-l/l5
  seconds
• A to D--0.99, once in a second
• A sharp to D sharp--l.05, twice in l-7/8
  seconds
• B to E--l.l2, twice in l-7/9 seconds

Table III
Temperament a la Williams of Gerrey

This lists the sequence of intervals which
I use, and accounts for the connections to
the synthesizer switch from the pins of the
organ chip as listed in the circuit. The
first note listed in the interval is the one
being tuned. At this time, the pitch control
of the filter can be adjusted; push the
reference tone button and tune it so that the
reference tone matches 4th octave A, either
from your fork or that on the piano.

Rather than tune a straightforward circle
of 4ths and 5ths (which would result in an
accumulated error over the whole sequence),
the second half of the circle is tuned in
reverse, using 3rd octave F as a secondary
standard. As a result, notes during one half
of the tuning are tuned just short of being
perfect (flat), while notes in the second
half are tuned just beyond being perfect
(sharp).

1. 5th octave C to a tuning fork, 523.3Hz.
2. Middle C to 5th octave C.
3. 3rd octave F, a secondary standard, to
   middle C (contracted interval, tuned
   sharp). Beats once in l-7/l0 seconds.

The following notes are tuned flat, short of
being perfect:

1. G to middle C, beats once in l-l/8
   seconds.
2. D to G, beats once in l-5/l0 seconds.
3. A to D, beats once a second.
4. E to A, beats once in l-l/3 seconds.
5. B to E, beats twice in l-7/9 seconds.

The following notes are tuned sharp, just
beyond the point of being perfect:

1. A sharp to F, beats once in l-l/4
   seconds.
2. D sharp to A sharp, beats twice in
   l-7/8 seconds.
3. G sharp to D sharp, beats once in
   1-3/7 seconds.
4. C sharp to G sharp, beats once in
   1-l/l5 seconds.
5. F sharp to C sharp, beats once in
   1-6/l0 seconds.
6. B to F sharp is a test; it should beat
   once every l-l/5 seconds.

Testing the Temperament

First of all, it
is essential that after the circle of intervals is completed, the beat of the last
interval (step l4) should agree with that
specified for the interval (in this case, a
4th from F sharp to B). Other intervals can
be tested along the way, such as major and
minor 3rds. Because beat rates for these
intervals are much faster, they are easier to
hear and no filter should be needed in order
to hear them.

I spot-check the sequence using major 3rds
as I go along. For example, as soon as step
6 is completed, the major 3rd from F to A can
be tested--it should flutter at 7 beats per
second--with its beat rate being compared to
the phrase "from Chicago to New York, from
Chicago to New York, . . ." A general progression of the 3rds' beat rates should be
looked for as the sequence of steps is
followed. At the very end, ascending major
3rds should have smoothly increasing beat
rates as you check on up through middle C
to E.

Parts List

Resistors
(carbon composition, l/4 watt, 5%)

• l--l0 ohm
• l--330 ohm
• l--5.6K
• 3--l0K
• l--47K
• l--l20K
• l--220K
• l--470K
• 1--1.5 meg

Resistors (metal film, exact values not
critical)

• l--l0K
• l--243K

Capacitors (disc ceramic)

• l--l000pF, 0.00luF
• 3--0.luF
• l--0.22uF

Capacitors (Mylar)

• 2--0.luF
• l--0.47uF

Capacitors (electrolytic, l2V)

• l--luF
• l--l0uF
• l--47uF
• 3--l00uF

Integrated Circuits

(all but the Reticon
filter are available from Jameco. The
Reticon filter is available from Applied
Invention, R.D. 2, Route 2l, Hillsdale, NY
l2529; phone 5l8-325-39ll).

• l--ICM-7555, Intersil CMOS 555 timer
• l--LM358
• l--LM386
• l--CD4046
• l--MK50240N
• l--R5620 Reticon filter

Front Panel Items

• l--Radio Shack 270-092A microphone
• l--Single-pole, l2-position switch, Radio
  Shack 275-1385
• l--DPST toggle
• l--SPDT pushbutton
• l--l0K volume control
• l--5K linear pot connected as rheostat
• l--Earphone jack

THE SMITH-KETTLEWELL
AUDIBLE STROBE TUNER

Abstract

In collaboration with Dr. T. V.
Cranmer, Director of Technical Services at
the Bureau for the Blind in Kentucky, we have
devised a tuning aid whose auditory feedback
is temporal in nature--the device "beeps" or
"buzzes" each time the unknown note from the
musical instrument drifts through a complete
cycle of phase relationships with a frequency
standard in the device. Three octaves of
standard pitches are selectable with switches
on the front panel. A microphone is placed
near or directly against the musical instrument. Auditory feedback from the tuning aid
is obtained either from its internal loudspeaker or through an earphone. If the
musical aspect of this project does not
interest you, portions of the circuit may
very well be of use; there is a dynamite
circuit for a crystal oscillator using NOR
gates, and the project well illustrates the
use of phase lock loops.

Introduction and Operation

It is a recognized fact that one's talent in playing a
musical instrument need not be accompanied by
the ability to service, maintain, or tune
instruments. For this reason, visual
"strobe-type" tuning aids are commercially
available; sighted musicians who need them
have access to devices which can provide
visual feedback as to when their instrument
is emitting proper pitches. Heretofore, an
equivalent tuning aid has not existed for use
by the blind; blind musicians have had the
matching of pitches by ear as their only
recourse. Since Tim Cranmer provided the
inspiration for developing this device, our
laboratory has nicknamed it the "Timmophone."

Our prototype was built into a so-called
"amplifier cabinet" such as the Radio Shack
270-269 measuring about 3-l/2 by 8 by 6
inches. This cabinet is large enough to
accommodate the rather large circuit board
(9 IC's mounted on perforated board and wired
point-to-point), as well as leaving room for
a l2-volt battery supply made of 8 C cells.

The front panel of our unit contains the
following controls:

1. A l3-position switch selects the note

   to which an instrument is to be tuned.
   (This switch selects l2 notes of the
   equally tempered scale including the
   octave; for example, A-440 through
   A-880.)

2. A 3-position octave switch puts the
   selected note into the appropriate
   octave; i.e., A-ll0 through A-220,
   A-220 through A-440, and A-440 through
   A-880.
3. A knob for controlling listening
   volume is provided; this control
   includes the on-off switch.
4. A toggle switch for squelch (to be
   discussed later) was included.
5. A "double mike jack" such as those
   found on tape recorders, was included;
   a l/8 inch jack accepts the microphone
   signal, while a l/l6 inch jack accommodates the microphone switch (the
   mike switch becomes a remote squelch).
6. Although our unit contained a loudspeaker, an earphone jack was
   provided; use of an earphone is
   recommended so as to avoid the problem
   of the device hearing itself.

In operation, the phase detector section of
a phase lock loop integrated circuit (PLL,
RCA type CD4046) is used to compare two
independent signals; one is the pitch of the
unknown note, and the other is a selected
note from the internal standard. As the two
input signals drift past each other in phase,
a clearly discernible signal is obtained from
a "lock-detection circuit" using a pair of
external NOR gates as recommended in the RCA
application notes on the PLL. To allow the
phase detection circuit to pass the internal
standard pitch when no signal is present at
the microphone, deliberate degradation of
performance of the "lock-detection circuit"
is assured by a low-value filter capacitance.

The internal pitch generator uses an organ
integrated circuit, which is clocked by a
crystal oscillator followed by two D flip-
flops as selectable octave dividers. This
organ IC is the "top octave chip" discussed
in David Plumlee's article, "Singing Chips,"
SKTF, Winter l982.

The microphone signal goes through a signal

processing section which is best called a
"pitch replicator"--it assures that the
fundamental frequency is presented as a clean
square wave to the phase detector. This
pitch replicator is composed of four sections
described as follows:

1. The microphone signal is first amplified by a two-stage preamplifier.
2. The input wave is then "squared up" in
   a Schmitt Trigger (using an RCA
   CA3l30). A Schmitt Trigger is a fancy
   term for a comparator using an op-amp
   with a slight amount of positive feedback to assure that it is bi-stable.
   An input signal has to overcome a
   certain amount of hysteresis as determined by the ratio of feedback to non-
   inverting input resistors.
3. A nonretriggerable tuned one-shot
   (using a 555 timer chip) assures that
   no doubling of input frequency can
   occur; zero crossings of the input
   wave at other than the fundamental
   period are ignored.
4. Finally, a PLL replicates input
   frequency and produces the necessary
   square wave for clean comparison in
   the phase detector to come later.

Because the phase detection circuit passes
the internal standard pitch when no signal is
present at the microphone, an optional
squelch circuit is included to interrupt the
audio output of the phase detector, and a
rectified signal from the microphone preamplifier is necessary to open the squelch.
A front panel toggle switch is provided to
defeat the squelch circuit, as well as making
this option available at the remote switch on
the microphone. (Defeating the squelch permits the tuning aid to emit a reference pitch
that the user can "aim for" in the initial
adjustment of his instrument.)

Because of the project's complexity, some
advice as to component layout may be warranted. (I certainly did it all wrong; what
follows is how I would proceed were I to do
it all over again.) The perforated "Vector"
board should be made as large as possible;
for example, a board whose dimensions are a
generous 3 inches wide by 7-3/4 inches long
can be secured to the rear panel of the
cabinet (exact dimensions are not critical).

It is probably wise to run bus strips along
each edge, which are tied together and considered ground. Another bus strip running
lengthwise along the middle of the board can
be the VCC line.

With the component side toward you, my
inclination would be to put the microphone
preamp and squelch rectifier at the upper
right corner, with the 3l30 Schmitt trigger
placed just below the VCC strip. The 3l30
circuit is simple enough to leave room for
the squelch transistor below it in the lower
right corner. To the left of the 3l30 can be
placed a 555 tuned one-shot, leaving room
below it for at least one of its timing
capacitors. Above the 555 and above the VCC
line (to the left of the mike preamp), the
PLL for the pitch replicator can be placed.

To the left of the 555, I would then mount
the PLL chip which is used only for its phase
detector. Directly above it and on the other
side of the VCC line, the 400l NOR gate chip
can be positioned. Components of the crystal
oscillator associated with this NOR gate

package will take up some acreage; these can
be fit into the space immediately to its left
and above the VCC line.

An efficient use of space might then
dictate that the LM386 audio amplifier be
placed directly below the components of the
crystal oscillator and to the left of the
phase detector PLL. Finally, the 40l3 flip-
flops can then be placed to the left of the
crystal oscillator, with the organ chip put
on the other side of the VCC line directly
below the flip-flops.

The above suggestions will work best if the
chips are oriented at right angles to the
length of the board, as opposed to placing
their in-line pins along the board's length.

These suggestions are offered for convenience, and not because the layout is
critical; I had crystal oscillator and clock
signals running lengthwise from end to end
with such abandon as to be embarrassing.

The switches used were Centralab
"Universal" types whose number of usable
positions is mechanically set by moving metal
tabs. For example, the l3-position unit is
actually capable of working through l7 positions, and the 3-position unit can be expanded to 5 positions. When mechanically
restricted to the number of positions noted,
free "unused" positions can be used as tie
points for components of the tuned one-shot.
For example, position 5 on one of the poles
of the octave switch was used to return two
of the timing capacitors to ground, and positions l6 and l7 on one deck of the note
selector were tied together and used as a
common connection for the six 555 charging
resistors.

The wafers of the Centralab switches are
very, very fragile. In cutting and filing
the shaft of the note selector to the right
length, I broke one of its wafers simply
holding it in my hand. Be careful!

While the squelch switch can be a simple
on-off toggle unit, a fancier 3-position
switch was used in our prototype. This unit
had a center "off" position, a "momentary"
(spring-return) action in one direction, and
a standard snap action toggle operation in
the other direction. The two positions were
jumpered together so that moving in either
direction closed the switch. Whether using
the microphone remote switch or the toggle,
closing the switch disables the squelch and
allows the note to be heard.

The double mike jack can be made by
mounting a l/8 inch unit and a l/l6 inch unit
close together. A standard spacing for such
microphone plugs is l centimeter between
centers of the holes. If metric measuring
instruments are not part of your tool collection, it is a handy thing to note that l
centimeter is very close to 4/l0 of an inch.
I made my pair of holes using l/l0 inch
perforated Vector board as a guide.

I actually had trouble with noise due to
ground loops when I secured both the microphone and earphone jacks to the cabinet. (As
soon as I touched them both to the chassis,
the organ tones became burbly.) The only way
I could cure the problem was to mount the
speaker jack with insulating "shoulder
washers" to isolate it from chassis ground.

Circuit

The negative side of the l2-volt
battery is grounded, while its positive
terminal goes through the on-off switch
(contained on the volume control) to the VCC
line. The VCC line is bypassed to ground by
250uF (negative at ground). The sleeve and
the switch contact of the microphone jack
(l/8 inch closed-circuit) are tied together
and go to ground.

The hot mike lead goes through luF (negative toward the mike), then through 2.21K
(metal film) to the inverting input, pin 6,
of an LM358 dual op-amp. The non-inverting
input, pin 5, goes to VREF (to be discussed
later). A feedback resistor of 332K (metal
film) goes from pin 7 to pin 6 of this op-
amp. The output, pin 7, goes through 2.2K to
the inverting input of the second op-amp, pin
2 of the LM358. The non-inverting input, pin
3, goes to VREF. This second stage has a
feedback resistor of 330K from pin l to pin
2. (These latter resistors are carbon composition.) Pin 4 of the LM358 is grounded,
while pin 8 goes to the VCC line.

The output of the second op-amp, pin l of
the LM358, goes through l00K to the inverting
input, pin 2, of a CA3l30 used as a comparator (Schmitt trigger). The non-inverting
input, pin 3, goes through l00K to VREF.
This comparator has positive feedback; a 470K
resistor goes from output to non-inverting
input, from pin 6 to pin 3 of the 3l30. Pin
4 of the 3l30 is grounded, while pin 7 goes
to the VCC line.

The output of the Schmitt trigger, pin 6 of
the 3l30, goes to pin 2 of a 555. Pin l of
the 555 is grounded, while pins 4 and 8 both
go to the VCC line. A 0.luF capacitor goes
between pins l and 8, located close to the
chip.

Pin 6 of the 555 goes through 0.022uF
(Mylar) to ground. Pin 6 also goes to the
arm of one pole on the octave switch. Position 3 of this pole is left open, position 2
goes through another 0.022uF Mylar capacitor
to ground, and position 1 goes through a
0.068uF Mylar capacitor to ground. (On the
switch wafer, the unused position 5 is
grounded and is used to secure these latter
two capacitors.)

Pin 7 of the 555 goes through 2.2K to pin
6. Pin 6 also goes to the arm of a pole on
the note selector. The following resistors
go from their respective positions on this
pole to VCC:

• Positions l and 2 are tied together and
  go through 75K to VCC.
• Positions 3 and 4 go through 62K to
  VCC.
• Positions 5 and 6 go through 56K to
  VCC.
• Positions 7 and 8 go through 47K to VCC.
• Positions 9 and l0 go through 43K to
  VCC.
• Positions ll, l2, and l3 are tied
  together and go through 39K to VCC.

(The unused positions l6 and l7 are tied
together and go to VCC--they are used to
secure one end of each of these resistors.)

Pin 3 of the 555 goes to pin l4 of the PLL
(RCA CD4046). Pin 8 of the PLL is grounded,
while pin l6 goes to VCC. Pin l5, a Zener
diode in the chip, goes through 47K to VCC,
as well as going through l0uF to ground
(negative at ground). This pin l5 is the
aforementioned VREF.

Pins 3 and 4 of the PLL are tied together.
Pin ll goes through 47K to ground. Between
pins 6 and 7 is 0.033uF. Pin 5 is grounded.

Pin l3 of the PLL goes through 330K, then
through 56K, then through 0.47uF to ground.
The junction of these two resistors goes to
pin 9. Pin 4 of this chip is the output of
the pitch replicator.

Another PLL chip (4046) is used strictly
for its phase detector. Pin 8 is grounded,
while pin l6 goes to VCC. To disable the
oscillator, pin 5 goes to VCC, while pin 9 is
grounded. Pin 4 of the pitch replicator (the
previous PLL) goes to pin 3, one phase detector input, of this latter IC. Pin l4, the
other phase detector input, goes to the arm
on the main deck of the note selector.

The audible signal is gotten off a modified
lock detection circuit on the latter PLL
chip. CD400l NOR gates are used; pin 7 of
the 400l is grounded, while pin l4 goes to
VCC.

Pin l of the latter PLL goes to pin 8 of
the 400l. Pin 2 of the PLL goes to pin 9 of
the 400l. Pin l0, the NOR gate's output,
goes through l00K, then through 0.005uF to
ground. This l00K resistor is shunted by a
lN9l4 diode (anode toward the 400l). The
junction of the diode cathode, the resistor
and the capacitor, goes to pin l2 of the NOR
gate. (While this second NOR gate is simply
a buffer, its pin l3 input is operated by the
squelch.)

Pin ll, the output of the second NOR gate,
goes through 0.05uF, then through 470K to
the top of a l0K volume control. The bottom
of this control is grounded. The arm goes
to pin 3 of an LM386. Pins 2 and 4 are
grounded, while pin 6 goes through l0 ohms to
VCC. Pin 6 is also bypassed to ground by
250uF (negative at ground). Pin 7 goes
through 25uF to ground (negative at ground).

To suppress oscillations, 0.22uF is connected between pins 4 and 5, very close to
the chip. Pin 5 goes through l00uF to the
tip of the earphone jack (positive toward pin
5). The sleeve of the earphone jack is
grounded. One side of the speaker goes to
the sleeve, while the other side goes to the
switch contact on the jack.

Two NOR gates are used for the crystal
oscillator; one is used for the oscillator,
while the other is simply a buffer. Pins l
and 2 of the 400l are tied together and go
through 22 megohms to pin 3. Pins l and 2
also go through a 24pF mica capacitor to
ground. Pins l and 2 also go to one side of
the crystal. Pin 3, the output of the first
gate, goes through 22K, then through a l50pF
mica capacitor to ground. The junction of
the 22K and l50pF goes to the other side of
the crystal. (The crystal is designed for
32pF shunt capacitance, and has a fundamental
frequency of 2l0.3kHz.)

Pin 3 of the 400l goes to pins 5 and 6 on
the same chip, with pin 4 being the buffered
output of the crystal oscillator. This pin 4
goes to position 3 on the second pole of the
octave switch, as well as going to pin 3 of a
dual-D flip-flop (CD40l3).

Pin 7 of the 40l3 is grounded, while pin l4
goes to VCC. The various "sets" and "pre-
sets" are all grounded, pins 4, 6, 8, and l0.
To make the flip-flops toggle, each section
has its D terminal going to its own Q bar;
pin 5 to pin 2, and pin 9 to pin l2.
Finally, the flip-flops are connected in
cascade; pin l, the output of the first, goes
to pin ll, the clock of the second.

Pin l of the 40l3, the output of the first
flip-flop, goes to position 2 on the octave
switch. Pin l3, the output of the second
flip-flop, goes to position l of the octave
switch. As mentioned, position 3 of this
pole on the octave switch goes to the output
of the crystal oscillator.

The arm of this pole on the octave switch
goes to the clock input, pin 2, of the
MK50240 organ chip. Pin 3 of the organ chip
is grounded, while pin l goes to VCC. The
following pins on the organ chip go to their
respective positions on the note selector
switch:

• Pin l6 goes to position l.
• Pin 4 goes to position 2.
• Pin 5 goes to position 3.
• Pin 6 goes to position 4.
• Pin 7 goes to position 5.
• Pin 8 goes to position 6.
• Pin 9 goes to position 7.
• Pin l0 goes to position 8.
• Pin ll goes to position 9.
• Pin l2 goes to position l0.
• Pin l3 goes to position ll.
• Pin l4 goes to position l2.
• Pin l5 goes to position l3.

As mentioned earlier, the arm of this pole
on the selector switch goes to the pin l4
input of the phase detector PLL.

Pin l3 of the 400l goes through 47K to VCC,
and pin l3 also goes to the collector of a
2N2222. The emitter of the 2222 is grounded.
Its base goes through 22K to ground.

Pin l of the LM358 (the output of the dual
stage mike preamp) goes through 2.2K, then
through luF (positive toward the resistor),
then to the cathode of a diode (lN9l4), the
anode of this diode being grounded. The
junction of the capacitor and the diode's
cathode goes to the anode of another lN9l4
diode; the cathode of this diode goes through
luF to ground (negative at ground). The
positive end of this latter capacitor goes
through l00K to the base of the 2N2222.

The collector of the 2N2222 goes to the tip
of the "remote" jack, with the sleeve of this
jack being grounded. This jack is shunted by
a toggle switch on the front panel.

Model II

Two improvements to the design of this
instrument bear considering. First of all,
the squelch rectifier off the output of the
mike preamp is somewhat particular about the
wave shape of the musical instrument.
Secondly, the device could be made more
sensitive to the "out of tune" condition.
Embellishments on the circuit which might
improve performance are listed below:

Squelch

As it stands now, some instruments
require that the microphone be placed very
close to or in direct contact with them in
order to open the squelch; this is true
because of asymmetry in their wave shape (at
present, the rectification scheme is half
wave).

One could try using a full-wave rectifier
to detect the audio signal. A good start
would be to try the "absolute value circuit"
in Al Alden's "Op-Amps" article in the Spring
l983 issue.

Another idea might be to get the squelch
voltage elsewhere in the circuit. For example, it might be possible to use the VCO
signal from the first PLL to open the
squelch; when this PLL replicates a frequency, a voltage will appear on pin l0 (a
buffered version of the VCO input). (Pin l0
needs a load resistor to ground in order to
function.) First try the simple idea of
running pin l0 of the PLL through l0K to the
base of the 2222. A problem to anticipate is
that at low frequencies (with the octave
switch in position l), there might not be
enough voltage to bias the transistor on.

Instrument Sensitivity

As it stands now,
this device beeps once every time the musical
instrument goes through a complete cycle of
phase crossing with the internal standard.
It would be a simple matter to double this
rate of "beeping" for a given out-of-tune
condition.

This modification would simply require that
the phase comparisons be done an octave high.
Both the standard and the pitch replicator
must be changed to accomplish this end.
First of all, double the crystal frequency so
as to run the organ chip and its octave
dividers at the higher frequency. Second, it
is a simple matter to make the pitch replicator PLL into a frequency multiplier by
inserting a flip-flop (divider) between pins
4 and 3. (Of course, the value of either the
VCO's resistor or its capacitor must be cut
in half so as to permit the PLL to cover this
higher range.)

In principle, this approach could be
carried to extremes by multiplying the two
frequencies by any number, but the beeps from
the phase detector would soon be out of audible range. (You might have to reduce the
value of the 0.005uF capacitor in the lock
detection circuit in order to pass the higher
frequencies of the beeps.) The main disadvantage in this scheme is that with the
squelch disabled the note you hear will be
that of the organ chip an octave higher than
the musical instrument in the above example.

Parts List

Capacitors (mica):

• l--24pF
• l--l50pF

Capacitors (Mylar):

• 2--0.022uF
• l--0.068uF
• l--0.47uF

Capacitors (disc ceramic):

• l--0.005uF
• l--0.033uF
• l--0.05uF
• l--0.luF
• l--0.22uF

Capacitors (electrolytic, l2V):

• 3--luF
• l--l0uF
• l--25uF
• l--l00uF
• 2--250uF

Resistors (metal film)

• 1--2.21K
• 1--332K

Resistors (l/4 watt, carbon composition, 5%):

• l--l0 ohms
• 3--2.2K
• 2--22K
• l--39K
• l--43K
• 4--47K
• 2--56K
• l--62K
• l--75K
• 4--l00K
• 2--330K
• 2--470K
• 1--22 meg

Semiconductors

(available from Jameco
Electronics, l355 Shoreway Rd., Belmont, CA
94002; phone: 4l5-592-8097):

• 3--lN9l4, lN4l48, anything
• l--2N2222
• l--LM358
• l--LM386
• l--NE555
• l--CA3l30
• l--CD400l
• l--CD40l3
• 2--CD4046
• l--MK50240N

Crystal

(available from your favorite crystal
company; for example, International Crystal
Company, P.O. Box 26330, Oklahoma City, OK
73l26; phone: 405-236-374l).

• l--2l0.3kHz, for 32pF shunt capacitors

Jacks and Switches

(available from Newark
Electronics, 500 N. Pulaski Rd., Chicago, IL
60624; phone: 3l2-638-44ll)

• 2--l/8 inch closed-circuit miniature
  phone jacks
• l--l/l6 inch open-circuit subminiature
  phone jack
• l--l0K volume control with switch
• l--Toggle switch (we used a 3-position
  unit, one of which was momentary; see
  text)
• l--Two-pole, 3-position (we used
  Centralab PA-4003 2-5 positions,
  Newark 57F933)
• l--Two-deck, l3-position (we used
  Centralab PA-3003 2-l7 positions,
  Newark 57F925)

Cabinet:

• l--"Amplifier Cabinet" such as the Radio
  Shack 270-269 or other suitable unit

EDITOR'S CORNER

A Debt Paid to Heritage

Having grown up in a piano store, the
option of pursuing this field as my career
was always open. As I reached adolescence
and began to seek career advice, however,
there were those among my counselors who
actively discouraged me from taking that
road, partly because the profits made are
small and partly because it is such a traditional occupation for the blind as to be a
stereotype. Though my ultimate career choice
was not the piano business, I am proud of my
engineering projects in support of it (an
audible vacuum gauge for repair of player
pianos and the piano tuning training aid of
this issue). Financially speaking (even for
the moonlighting amateur like me), the practice of the craft is flexible enough so as to
save our bacon every once in a while, and I

would like to speak a moment in defense of
it.

No doubt the emergence of low-cost portable
keyboard instruments will cut into the
piano's ultimate role in the music business.
However, although I cannot verify it, I have
heard that more pianos were being made in
this decade than at any other time in
history. In any case, there are millions of
them, 98 percent are out of tune, and well
over half need the touch of a craftsman to
put them in good working order. Being a
qualified piano technician is a craft which
is almost depression-proof; canvassing
churches, schools, and residential neighborhoods will generally find you work, and in
the worst of times you can always barter
tunings for meals. (By the same token, you
will never get rich; the profits are low and
you will burn up at least a third of them in
paying a driver.) Finally, making something
sound good and work properly is always
rewarding.

My sentimental attachment to the field is
very personal. It goes back to a father
teaching his small child--not out of patient
indulgence, but out of genuine enthusiasm--
the principles of bearings and springs, the
relationships of levers, the properties of
various materials, and the elements of harmonic physics. To that shop I owe my basic
mechanical aptitudes which were nurtured at
an early age. To that shop I owe my basic
understanding of running a small business.
To that shop I owe my college education and
the financing of my house. I have said
before that I owe my career choice to Braille
Technical Press and to its constituents. To

the piano shop I owe the fact that I grew up
in what they now call an "enriched environment" (known to be an advantage in child
development); from that environment I got the
basic skills of my employability.

A lot goes into an invention, such as my
piano tuning filter. It took Al Alden to
find for me the filter chip. Al Alden taught
me everything I know about phase lock loops.
By reading my own magazine ("Singing Chips"
by David Plumlee, Winter l982), I learned of
the organ chip with which I could clock the
filter. It turns out that the basic experiment of using such a device was done a
century ago by Helmholtz. (Buckminster
Fuller once said that all of his better ideas
had a mustiness about them.)

Yet, in a little black box called the
"Smith-Kettlewell Training Aid for Piano
Tuners" is something undeniably mine, a
device to ease the training of new
apprentices.

Of utmost importance is my work for this
magazine; it is, no doubt, my contribution of
highest impact. However, as far as engineering projects are concerned, my instruments
for piano work are those by which I would
most like to be remembered.

* * * * * * * * * * * * * *

Confidential Memorandum to Braille
and Talking Book Readers:

The reason this issue is ever-so-slightly
delayed is that I shattered an ankle in late
Spring, and am dictating it over phone lines
from my wheelchair. By the time you receive
this, I will no doubt be walking again.
Sssssshhhhhh--the official story around work
is, "The doctor says he might/can hitch
himself up on one elbow by Christmas!" In
any case, this issue is a good one; what's
worth having is worth waiting for.

Sincerely,

Your Monopeditor