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February 1953 QST Article

## February 1953 QSTThese articles are scanned and OCRed from old editions of the ARRL's QST magazine. Here is a list of the QST articles I have already posted. All copyrights are hereby acknowledged. |

James Kilton Clapp in 1948 first published details on an oscillator
that used positive feedback obtained from an LC
(capacitive & inductive) voltage
divider to initiate and sustain oscillations. Thus was born the
now familiar Clapp oscillator. It had an advantage over both the
Colpitts and Hartley oscillators because the feedback, not being
dependent on a simple capacitive or inductive voltage division,
respectively, made it more reliable as a variable frequency oscillator
(VFO). This article does a nice job
of explaining the operation of the Clapp oscillator. Just as the
Colpitts and Hartley oscillators handily provide an easy mnemonic
for being based on voltage dividers of **
c**apacitance
with the

*An Explanation of the Series-Tuned Colpitts Circuit *

By Rex Cassey,* ZL2IQ

In this article, ZL2IQ discusses the principles behind the popular Clapp VFO circuit, and applies the theory to practice. A discussion of the "remotely-tuned" Clapp is included.

Many of the peculiar results obtained with the Clapp oscillator
can be explained by a simplified analysis of the circuit, such as
the one given below based on the work of Sandeman of the B.B.C.^{1}
Give it a few minutes' study and you'll be surprised how many improvements
you can make on your oscillator!

The basic r.f, circuit for the Clapp oscillator is shown in Fig.
1. The oscillatory circuit consists of the series-tuned circuit
L_{1}C_{1} together with its loss resistance R,
and the feed-back condensers C_{2} and C_{3}. The
condition where the feed-back energy balances out the losses in
the circuit, i.e., the condition for oscillations to occur, is given
by

R = - g_{m}X_{2}X_{3}
(see Appendix), (1)

where X_{2} and X_{3} are the reactances, respectively
of C_{2} and C_{3}.

The condition determining the frequency of oscillation is given by

(see Appendix).

Just take another look at that formula (2) above. What does it
tell you? Sure - the frequency of oscillation; but that's not all
by a long shot. It also tells you how to make your oscillator have
high stability! Take a good look at that expression under the square-root
sign on the right. It includes C_{2} and C_{3},
the feed-back condensers. The value of the effective capacitance
of these two condensers will change as the loading of the oscillator
is varied, since they have the effective grid-cathode and plate-cathode
capacitance in parallel with them. However, the resultant changes
in frequency will be quite small because of the effect of that square-root
sign. If we make the tuning capacitance, C_{1}, small and
the feed-back condensers large, the expression under the square-root
sign will be very nearly unity, and the frequency becomes relatively
independent of the feed-back condensers and dependent only on the
series-tuned circuit, L_{1}C_{1}. Hence, dynamic
instability attributable to change in tube capacitance is effectively
eliminated.

What else can we find out from that expression under the root
sign? One thing is that it can tell us why the oscillator is often
called the" series-tuned Colpitts." It will be seen that the expression
never quite reaches unity, but is always slightly larger. Putting
it another way, the oscillator frequency can never be the same as
that of the series-tuned circuit alone, but is always slightly higher.
If it were the same as the resonant frequency of the series circuit,
we would have merely a pure resistance of value R across the e_{1}
terminals of Fig. 1. We would not expect the circuit to oscillate
in that case. However, at a higher frequency the reactance of the
series circuit will be positive and it will look like a small inductance
across the terminals. This is equivalent to the circuit condition
we have in the normal Colpitts! Are the Colpitts and Clapp oscillators
the same? No. Thanks to "Cathode Ray" with his reactance-frequency
diagrams," this has been made abundantly clear. Briefly, if we used
only an inductance, the inductive reactance across the el terminals
would vary very slowly with change in frequency. By using a series
circuit, L_{1}C_{1}, however, a small change in
frequency causes a large change in the inductive reactance across
the terminals and hence an extremely small change in frequency will
be sufficient to counteract any change in the phase shift taking
place around the feed-back loop. The stability is therefore very
much higher than can be obtained with the normal Colpitts - probably
at least 100 times more so.

There is one other difference which may be mentioned as a matter
of interest. In the Colpitts we generally tune by varying the value
of the feed-back condensers, C_{2} and C_{3}, whereas
in the Clapp circuit we vary the "effective" inductance by altering
the series-tuning capacitance. However, the essential difference
does not lie in the method used for tuning, but in the method of
providing the effective inductance in the oscillatory circuit.

Now take a look at that other formula marked (1) above. What
can you deduce from it? Yes, sir, this one's the 64-dollar question.
And the answer is that if the value of the expression on the right-hand
side is less than the value of R, the circuit just doesn't oscillate.
If the right-hand side is greater than R, the circuit will oscillate
and the grid current will flow. As grid current increases, the operating
g_{m} falls until the value of the expression on the right-hand
side equals R, when stable oscillations result. There's one thing
in particular you should notice in that formula. You may have the
idea that if you increase the Q of the coil, the efficiency and
output of the oscillator will be improved. But take another look
at formula (1). It's not the Q of the coil that's the important
factor but the value of the loss resistance R. If you put in a coil
with a higher inductance and a higher Q, the efficiency won't be
improved unless the loss resistance has been lowered in the process.

Now let's look at some of the problems you can solve by this "oscillation formula."

In (B), two cables are used between the feed-back condensers and the tube. |

Some of the local gang have been telling you that the Clapp oscillator
is just the cat's pajamas for stability, so you decide to build
one. You were going to change from xtal to VFO before the Sweepstakes
Contest, anyway. Half an hour before the contest starts everything
is almost ready. You've checked the tuning range of the series circuit
with the grid-dip meter and the range is OK. Fine - you flip the
switch - and what happens? It doesn't oscillate. Wow! Better check
the plate voltage - where did I put that multimeter? Ah, yes, here
it is. Just over 300 volts and the ICAS rating is only 300. Should
be getting plenty output. Hmm. Maybe it's a dud tube. There's a
new one in the box at the top of the shelf there. Here she is -
plug it in and let it warm up a bit. Now flip the switch once more
- and what happens? No oscillations. Hmmm. This is going to be a
job for the soldering iron. It's also a job where a look at that
"oscillation formula" can be mighty useful. On the left-hand side
of formula (1) we have the loss resistance. We could reduce it in
various ways. For example, we could raise the Q of the existing
coil by removing the shield can and replacing it with a bigger one.
This would result in a lower value of loss resistance, which is
what we want. We could prune some turns off the coil, but this would
mean that the series-tuning condenser would be bigger, but we have
already seen that this may reduce the stability slightly. What about
the expression on the right-hand side of the formula? The first
part is the g_{m} of the valve. We've got the correct voltages
for the plate (and screen) applied so we can't very well increase
it to make g_{m} bigger. We might be able to use another
value of cathode or grid resistor, though. What else have we that
can be varied? The only other terms in the formula are the reactance
of the feed-back condensers. We could increase the reactance by
putting in smaller values of feed-back condensers, although this
would reduce the frequency stability slightly as we have already
seen in connection with formula (2). This would be the easiest way
to make the circuit oscillate; but the best way would be to reduce
the loss resistance in the series-tuned circuit.

You take a look at the clock and find that there's still 10 minutes to go before the contest starts, so you decide to reduce the values of the feed-back condensers. A moment's work with the soldering iron and the job is done. You flip the switch once more, and - bibbety-boppety-boo - it goes!

Nice timing - still 5 minutes to go before the contest starts.
You check the setting for the low-frequency end of the band and
then swing the dial to check the high frequency end and suddenly
"plop" - no oscillation. Down again and it's OK. Up again and it
stops. Why? Well, the only term in the oscillation formula which
is dependent on frequency is the reactance of the feed-back condensers.
At the higher frequency the reactance is lower and the g_{m}
would have to rise to counteract the effect. Another quick change
is made. With a lower value of feed-back condenser, everything is
OK, and you're off to a flying start in that contest after all.
When it's over, you'll have time to think out ways and means of
reducing that loss resistance in the tuned circuit so that the value
of feed-back condensers can be increased.

One point, which we have not considered so far in our discussions,
is the desirability, or otherwise, of using a grid-blocking condenser
such as C_{4} in Fig. 2. It is certainly not necessary for
the purpose of blocking the high voltage from the grid of the tube;
this is effectively done by the series-tuning capacitance, C_{1}.
Does the inclusion of the grid condenser have any undesirable effect
on the operation of the oscillator? The answer can be found by an
extension of our simplified analysis of the circuit. In the analysis,
we assumed that the grid voltage was equal to i_{1}X_{2}.
However, if C_{4} is included in the circuit, only a portion
of the voltage across C_{2} will be applied to the grid,
since C_{4} and the grid-cathode capacitance of the tube
now form a voltage-divider network across the feed-back condenser.
If the appropriate change is made throughout the analysis, it will
be found that the right-hand side of formula (1) is multiplied by
a factor of C_{4}/(C_{4} + C_{gc}), while
the frequency formula (2) remains unchanged. If the grid condenser
is very much larger than the grid-cathode capacitance of the tube,
its effect may be neglected. However, it must be remembered that
under operating conditions, the grid-cathode capacitance may be
as much as 30 or 40 times the static value. In the case of a triode,
it may be as high as 100 μμfd. as a result of the Miller effect,
with a 100-μμfd. condenser for C_{4}, only half the
voltage would be applied to the grid. In this case the circuit would
not oscillate so readily and it may be necessary to reduce the value
of the feed-back condensers to offset the effect, with a resultant
loss in stability. In general, we deduce that the grid-blocking
condenser is undesirable in the case of a triode, since it reduces
the efficiency and stability of the oscillator. In the case of a
pentode it has little effect but is still an unnecessary element
in the circuit.

Since this dissertation has been prepared as a result of reading
a very interesting article by W3ASW in August QST,^{3} it
may be of interest to comment on the effects found in the remote-controlled
VFO which he described. The appropriate circuits are shown in Fig.
2.

In a description by W9ERN of a somewhat similar arrangement.^{4}
it has been pointed out that 70-ohm coaxial cable has a capacitance
of about 20 JLJLfd. per foot. Two lO-foot lengths were, in fact,
used by W9ERN in place of C2 and C3• In the circuits shown in Fig.
2, each of the lengths of coaxial cable would have a capacitance
of about 125 μμfd. The effect of this additional capacitance
will depend on how it is introduced into the circuit and a number
of cases are shown in Fig. 3. The circuit in A shows the normal
condition, while those in B, C, and D contain added capacitance.
In the normal case A, the effective capacitance which has been placed
across the series-tuned circuit is 250 μμfd. For the other
circuits, this value will be found to have been increased to 313,
375, and 405 μμfd., respectively. In the case of B, the values
of X_{2} and X_{3} in our oscillation formula (1)
above will have been reduced and the circuit will not oscillate
so readily. The original conditions could be obtained by simply
reducing the 500-μμfd. condensers to 375 μμfd. This
is effectively the arrangement used by W9ERN in his oscillator circuit.
However, in order to use this arrangement, a grounded-cathode oscillator
circuit must be adopted. This does not present any difficulty.

In the case of C, which is equivalent to Fig. 2B, and in the
case of D, which is equivalent to Fig. 2A, it will be noticed that
the feed-back condensers have been by-passed by the 125-μμfd.
capacitance of one of the coaxial cables. This results in a portion
of the current i_{1}, which flows in the oscillator circuit,
being ineffective insofar as the production of grid voltage across
C_{2} is concerned, and hence lowers the efficiency of the
oscillator. If we increase the current flowing in the series-tuned
circuit to make up for this by-passing effect, more energy will
be lost in the resistance of the series-tuned circuit and this will
tend to offset the improvement we may have made. Looked at from
another point of view, the effect is similar to that of adding capacitance
across a crystal holder, a practice which we know from experience
to be undesirable.

Mention has been made by W3ASW of the apparently excessive loss in the coaxial cables when they are inserted between the series-tuned circuit and the feed-back condensers. This may have been a result of the increased current brought about by the by-passing effect of the coaxial cables. In his final circuit arrangement, the majority of the circulating current has been confined to the remote control box by placing the lumped capacitance of the feed-back condensers in that position, so that any losses in the coaxial cables should have been reduced.

In closing, here's hoping I'll be seeing you on 7023 kc. some time. Yes, I'm "rock bound," but not for long (I hope) now that I know where to look for some of the bugs that are going to arise when I build that new Clapp VFO oscillator!

**Appendix **

Suppose that an r.f. current, i_{1}, is flowing around
the circuit in the direction shown. The voltage developed across
the terminals 1-1, is equal to i_{1}z_{1} that is,

Consider now the voltage developed across the feed-back condensers across the terminals 2-2. Let the plate current be

i_{2} = g_{m}e_{g} = g_{m}(i_{1}jX_{2}).

The voltage developed across the feed-back condensers will be the sum of the voltages produced by the two currents which are flowing.

That is,

If the two voltages we have found above are exactly equal, we
have the normal condition for stable oscillations in the circuit.
If we equate the two expressions we have found for the voltages,
and cancel out the term i_{1}, since it is common to both
sides, we get

If we equate the real terms in the above expression, we get

R = - g_{m}X_{2}X_{3}. (1)

Equating the imaginary terms now,

(2)

*92 Amritsar St., Wellington, N. Z.

1 E. K. Sandeman, Radio Engineering, Vol. I, p. 421,1947.

2 Cathode Ray, "Series or Parallel," Wireless World, August, 1952, p. 321.

3 Long, "Cutting Down VFO Drift," QST, August, 1952, p.20.

4 Clemens, "The R.C.O. - A Remote Control Oscillator," Radio & Television News, August, 1952, p. 40.

Posted May 8, 2015