February 1953 QST
Table
of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from
QST, published December 1915  present (visit ARRL
for info). All copyrights 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 capacitance
with the Colpitts
oscillator and inductance (Henries) with the
Hartley
oscillator, the Clapp
oscillator is based on both
capacitance and
inductance (Henries).
The Clapp Oscillator  and How!
An Explanation of the SeriesTuned 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 "remotelytuned"
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!
Fig. 1  Basic Clapp oscillator circuit.

The basic r.f, circuit for the Clapp oscillator is shown in Fig. 1. The
oscillatory circuit consists of the seriestuned circuit L_{1}C_{1}
together with its loss resistance R, and the feedback condensers C_{2}
and C_{3}. The condition where the feedback 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 squareroot sign on the right. It includes C_{2} and C_{3},
the feedback 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
gridcathode and platecathode capacitance in parallel with them. However, the resultant
changes in frequency will be quite small because of the effect of that squareroot
sign. If we make the tuning capacitance, C_{1}, small and the feedback
condensers large, the expression under the squareroot sign will be very nearly
unity, and the frequency becomes relatively independent of the feedback condensers
and dependent only on the seriestuned 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" seriestuned 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 seriestuned 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 reactancefrequency 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 feedback 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 feedback condensers,
C_{2} and C_{3}, whereas in the Clapp circuit we vary the "effective"
inductance by altering the seriestuning 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 64dollar question. And the answer is that if the value
of the expression on the righthand side is less than the value of R, the circuit
just doesn't oscillate. If the righthand 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 righthand 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."
Fig. 2  Circuits using remote frequency control. In the
circuit of (A), a single coax conductor is used between the tuned circuit and the
feedback condensers.
In (B), two cables are used between the feedback 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 griddip 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 lefthand 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 seriestuning condenser would be bigger, but
we have already seen that this may reduce the stability slightly. What about the
expression on the righthand 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 feedback
condensers. We could increase the reactance by putting in smaller values of feedback
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 seriestuned 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 feedback condensers.
A moment's work with the soldering iron and the job is done. You flip the switch
once more, and  bibbetyboppetyboo  it goes!
Nice timing  still 5 minutes to go before the contest starts. You check the
setting for the lowfrequency 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 feedback 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 feedback
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 feedback condensers can
be increased.
One point, which we have not considered so far in our discussions, is the desirability,
or otherwise, of using a gridblocking 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 seriestuning 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 gridcathode capacitance of the tube now
form a voltagedivider network across the feedback condenser. If the appropriate
change is made throughout the analysis, it will be found that the righthand 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 gridcathode capacitance of the tube, its effect may be neglected.
However, it must be remembered that under operating conditions, the gridcathode
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 100μμfd. 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 feedback condensers to offset the effect,
with a resultant loss in stability. In general, we deduce that the gridblocking
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 remotecontrolled 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 70ohm coaxial cable has a capacitance of about 20 JLJLfd.
per foot. Two lOfoot 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 seriestuned 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 500μμfd. condensers to 375 μμfd. This is effectively
the arrangement used by W9ERN in his oscillator circuit. However, in order to use
this arrangement, a groundedcathode 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 feedback condensers
have been bypassed by the 125μμfd. 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 seriestuned circuit to make up for this bypassing effect,
more energy will be lost in the resistance of the seriestuned 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.
Fig. 3  The effect of additional cable capacitance across
the feedback condensers will depend upon where the capacitance is introduced. as
discussed in the text.

Mention has been made by W3ASW of the apparently excessive loss in the coaxial
cables when they are inserted between the seriestuned circuit and the feedback
condensers. This may have been a result of the increased current brought about by
the bypassing 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 feedback 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 11, is equal to
i_{1}z_{1} that is,
Consider now the voltage developed across the feedback condensers across the
terminals 22. Let the plate current be
i_{2} = g_{m}e_{g} = g_{m}(i_{1}jX_{2}).
The voltage developed across the feedback 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 September 20, 2021(original 5/8/2015)
