May 1931 RadioCraft
[Table of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from RadioCraft,
published 1929  1953. All copyrights are hereby acknowledged.

Open up a radio transceiver chassis
that operates below 300 MHz (VHF and lower), particularly one built before
the advent of highly integrated circuits, and you will almost certainly find many
transformers and inductors. Without the advantage of using microstrip type distributed
impedance matching, the use of wirewound transformers and inductors is your only
option for tuning filters and implementing interstage impedance matching. In the
days of vacuum tubes in all stages of a transmitter and/or receiver, transformers
were found in every stage from baseband through RF. Knowing how to design and build
efficient transformers was essential to proper operation. This circa 1931
RadioCraft magazine article
provided a basis for understanding the science of mutual inductance and magnetic
coupling.
Design of RadioFrequency Transformers
Fig. 1  In the standard screengrid amplifier stage, the
high plate resistance of V1 necessitates a high impedance in L1B and, therefore,
loose coupling into the tuned circuit L2BC2.
As modified by the problems which have been introduced by the multistage screengrid
amplifier
By Sylvan Harris
From the viewpoint of the designer of a radiofrequency amplifier which is to
be part of a radio receiver, when he has once determined the number of tuned and
untuned stages he wants to use and the amount of amplification he must have, there
remain really only three problems that he must solve. Assume therefore, that the
circuit arrangement of the amplifier is settled and the particular tubes chosen:
the designer then must determine 
(a) the proper voltages to use on the tubes and the manner of obtaining these
from the powerpack;
(b) the system of controlling volume and the location of the volumecontrol elements
in the circuit;
(c) the actual design of the radiofrequency transformers,
The determination of the tube voltages is more or less determined by the manufacturer's
ratings; which often must be somewhat modified by considerations of powerpack load,
crossmodulation effects, gridcircuit overload, etc. The selection of the system
of volume control is apart from the design of the amplifier proper; that is to say,
the system to be chosen is one which will have no effect on the tuning of the amplifier,
but will exert its control over sufficient range to enable the operator to reduce
the volume of the most powerful broadcaster to zero.
Fig. 2  The theoretical limit of screengrid amplification;
on the basis of 1000 micromhos of mutual conductance, and 0.02·mmf. gridplate capacity
in the screengrid tube.
Fig. 3  The maximum voltage amplification of a stage, plotted
against the mutual inductance of an output transformer of good quality. The closer
the coupling, the more unequal the gain.
Fig. 4  The curves of amplification here correspond to
those of Fig. 3; but are plotted against frequency, to show the greater efficiency
at the lowwave end of the broadcast band.
Fig. 5  A transformer designed to bring about more even
gain throughout the range of broadcast frequencies. LoCo is tuned to about 500
kc., or 600 meters; L1 is smaller.
Fig. 6  The characteristic curve of the transformer of
Fig. 5, due to the decreasing reactance of Co as the frequency rises.
Fig. 7  The completed radiofrequency transformer, designed to overcome
the disparity in amplification at the ends of the band. Lo is to be shunted by a
40·mmf. capacity.
Fig. 8  The slotwound primary loading coil Lo of the circuit
shown in Fig. 5, as applied to a standard R.F. transformer, The diameter of
the coil is very small.
Fig. 9  Curves obtained from a commercial antenna transformer: in (2),
the primary is smaller and the coupling is looser. Note that the vertical scale
is logarithmic.
Fig. 10  Selectivity curves at 1000 kc. of interstage coupler
(A) and aerial coupler (B). The former has the high tube resistance R1, and the
latter the high aerial capacity, in the primary circuit.
Fig. 11  Above, effect of frequency on a coil; the "dissipation
constant," inversely proportional to the resistance is the resultant of the effects
shown below and of the frequency itself, which is a straight slope.
Such matters are of course, quite intricate, but the analysis of each of the
several problems can be made somewhat more or less independently of each other;
and, after all, perhaps the most important problem of all is that of designing the
radiofrequency transformers.
We need hardly consider the tuning condensers at all. The design of these circuit
elements is practically fixed. The economics of condenser design have practically
fixed the number and size of the plates and the general arrangement of the frame
structure; so that there is not much that can be done in this matter.
Inductance Found by Experiment
Consequently, the first part of the problem of radiofrequency transformer design
is to calculate the inductance required to enable us to tune over the broadcast
range with the particular condenser capacity we intend to use. Of course, knowing
the required inductance value, only, is not sufficient; a coil must be constructed
which will have this inductance. This can best be done by cutandtry methods, backed
up by a certain amount of experience along this line.
In radiofrequency amplifiers designed around screengrid tubes, which have very
high plate resistances, the proportioning of the tuning inductance to cover the
tuning range involves only the secondary of the coil. In other words, with the tuning
condenser connected to the secondary, and with the coupling between the circuits
quite loose because of the high plate resistance of the tubes, the tuning range
is determined almost wholly by the secondary circuit, and independently of the primary.
(Of course, the separate capacities of the primary and secondary coils, as well
as their mutual capacity, have an influence on the tuning range; but this effect
should be interpreted as a variation in the secondary inductance rather than as
a coupling between the two circuits.)
At any rate, let us suppose we have determined all these things; we have fixed
the tube voltages, the tuning capacity and the secondary tuning inductance. We must
now consider the design of the primary circuit of the R.F. transformer. Fig. 1
shows the simple circuit of a tuned R.F. amplifier using screengrid tubes. The
first thing we must determine about this circuit, in order to assist us in our work
of transformer design, is how much voltage amplification per stage this amplifier
can handle.
We all know that, if we have too much gain per stage, the circuit will oscillate,
because of the feedback through the tubes, between the plates and grids. Of course,
we are using screengrid tubes, in which the grids are supposed to be screened from
the plates; but it must not be forgotten that this screening is not 100 percent
effective. Furthermore, there are other means of coupling between stages which are
conducive to regeneration and oscillation; so we must be careful not to make the
gain per stage too high.
Limit of Amplification
Fig. 2 shows the maximum gain per stage which can be used, assuming that
the only source of feedback is that which occurs within the tube between plate
and grid. In other words, if this were the only coupling we had between stages,
the gain shown in Fig. 2 is the maximum that could be used without having the
circuits oscillate. If there is external coupling between the stages (as for example,
in coupling resistors or condensers) the maximum amplification that can be used
is less than that shown in Fig. 2; how much less, depends upon the amount and
the kind of external coupling.
At any rate, as we can see in Fig. 2, we cannot expect a gain per stage
of much more than 80, in a threestage amplifier using type '24 tubes. This may
seem quite large; as a matter of fact it is large. It is extremely difficult to
realize a gain per stage of even 70 or 80 over the broadcast range, except in an
amplifier which is very well made, shielded, choked and bypassed with extreme care.
This, of course, is out of the question in commercial radio receivers, on account
of the cost involved. As a matter of fact, in welldesigned commercial receivers,
we can generally count on obtaining perhaps half the maximum possible gain; a limit
due to the interstage couplings external to the tubes.
The maximum possible gain is a function of the mutual conductance of the tube;
that is, the greater the mutual conductance, the greater the possible gain. (See
the article, "Mutual Conductance and Its Associates," March, 1931, RadioCraft.
 Editor.) On the other hand, the greater the number of stages, the lower the maximum
possible amplification. The same is true of the gridplate capacity of the tube;
to double it reduces the amplification thirty per cent.
We must now consider how much gain per stage we actually obtain in a typical
circuit. Of course, the actual gain depends on the mutual conductance of the tube,
the resistance of the tuned circuit (or the coil's "dissipation constant" Q), and
the coupling between the primary and secondary (M). The Rp of the tube also has
an effect on the gain, but this effect is quite small in screengrid tube circuits.
Mutual Inductance of the Coil
In Fig. 3 we have curves which show the relation between the mutual inductance
of the transformer and the voltage amplification obtained at different frequencies.
The value of the coil's dissipation constant Q (which is 6.28 x f x L/R2)
is here assumed to be 100; which is a fair value for commerciallydesigned coils
of good quality. On the basis, it can be seen from Fig. 3 that; at 1000 kc.,
we can expect an amplification of about 32 per stage if the mutual inductance is
50 microhenries. The curves show that, as we increase the mutual inductance, the
gain goes up steadily. This means that, if we double the primary turns, we will
double the gain; because the mutual inductance varies as the primary turns.
Another thing, which Fig. 3 teaches us, is that the voltage amplification
increases as we increase the frequency. This can, perhaps, be seen more clearly
by plotting the curves in a different manner, as in Fig. 4; here the voltage
amplification is shown plotted against the frequency, for various values of mutual
inductance. For example, if the mutual inductance is 50 microhenries, we can expect
a gain of 32 per stage at 1000 kc. as before. However, if we keep the mutual inductance
constant and increase the frequency, (tune to a lower wavelength), we see that the
gain rises steadily. This is the frequencycharacteristic which we obtain in all
radiofrequency amplifiers employing the simple twocoil R.F. transformer. At high
frequencies the gain is great, and at low frequencies it is small; and, the greater
the mutual inductance, the steeper the curve.
Problems of MultiStage Design
It must be remembered that the curves shown here are for a single stage. With
two stages, alike in design, the total amplification at any frequency is the square
of the amplification of one stage; if there are three stages, the total amplification
is the cube of that of one stage.
This means that, if we plotted the curves of Fig. 4 for three stages instead
of one, we should find the curves very much steeper; and the difficulty which designers
find in R.F. amplifiers would be more obvious. In a threestage amplifier, the R.F.
amplification at 1500 kilocycles may be as high as three to five times that obtained
at 550 kilocycles; or even more, depending upon the particular design. It is on
this account that attempts have been made to design R.F. transformers which will
give reduced amplification at the higher frequencies, and greater amplification
at the lower frequencies.
It is necessary, at the outset of such a design, to provide for keeping the coupling
sufficiently loose; so that the reaction of the primary circuit will not appreciably
affect the secondary tuning. This is a very necessary requirement, in order to make
it possible to tune the amplifier over the entire broadcast range, while avoiding
resonance effects, due to the primary, which would make the tuning of the secondary
uncertain at certain frequencies; such sometimes occur in the tuned circuit coupled
to the antenna, when very large antenna capacities are used, or when the antenna
coupling is very tight.
This being the condition  that the coupling between the primary and secondary
must be loose  it is clear that the way in which the amplification varies with
frequency will depend mainly upon the design of the primary circuit. Returning to
Fig. 3, it will be obvious that the amplification is dependent upon the mutual
inductance between the primary and secondary. Hence, if .we can make this mutual
inductance vary in any way which we desire, we may likewise be able to control the
amplification accordingly.
A Compensatory Coil Design
This is what is done in actual practice; in one design, illustrated in Fig. 5,
a local tuned circuit in the primary, consisting of a loading inductance Lo shunted
by a condenser Co, is placed in series with the regular primary L1. The secondary
L2B is of the usual design.
The selfinductance Lo is quite large compared with the inductance L1; so that
at low frequencies (as at 550 kc.) L1 has little effect in comparison. Lo and Co
are so proportioned that this local circuit is resonant at about 500 kilocycles,
just above the upper wavelength of the tuning range of the amplifier. The mutual
inductance Mo (between the coil Lo and the secondary L2) is opposed to the mutual
inductance M, between the primary L1 and the secondary L2. In other words, Lo and
L1 are arranged to "buck" each other. Now let us see what happens:
Suppose we tune to a long wave , L1 has little effect because it is a small inductance;
the signal current in the local tuned circuit LoCo is quite large, because we are
near the resonance frequency of the local circuit.
The signal energy is then transferred to the secondary via the mutual inductance
Mo, which can be so adjusted that the amplification is quite large.
Now, suppose we gradually tune to higher and higher frequencies. As the frequency
increases, it departs further and further from the resonant frequency of LoCo, and
Lo becomes a choke coil in effect. Co acts as a bypass condenser more and more,
as the frequency increases; so that the high impedance of Lo does not obstruct the
signal to any considerable amount.
Now the regular primary L1 begins to work, transferring power to the secondary
via the mutual inductance M. At very high frequencies, the system acts as if Lo
and Co were not present; since Co becomes an effective bypass. So this is an arrangement
which will provide great amplification at low frequencies, because of the resonance
effects in the primary, and, likewise, high amplification because of the usual laws
pertaining to the simple primary circuit L1. By combining these effects we obtain
a curve like that shown in Fig. 6  high at both ends and drooping slightly
near the middle. By properly proportioning the various windings, the drop in the
middle of the curve can be made small; and the curve will be as nearly linear as
can be practically desired.
There are various arrangements of this system, but all work on the same principles.
Sometimes the condenser Co is omitted, and the winding Lo is so made that its selfcapacity
(or distributed capacity) is sufficient to cause the resonance and bypassing effects.
The coil Lo may also be located at various points of the secondary, in different
designs. There is no rule which can be given. The whole effect is so complicated
that the only way in which to design such a system is to do it experimentally; that
is, use the cutandtry method.
Constructing the Transformer
Figs. 7 and 8 show the construction of such an R.F. transformer. The primary
loading inductance Lo is a randomwound coil of 400 turns of No. 36 D.S.C. wire
on a small bobbin, in a slot 3/16inch wide, and having an inside diameter of 1/2inch.
The construction of this bobbin is shown in Fig. 8.
The bobbin is inserted into the top end of the tubing on which the secondary
is wound; the latter winding starting just below the bobbin. At the lower end of
the secondary  away from the grid end  is wound the normal primary L1, upon a
laver of empire cloth; this part of the construction is quite usual. The coil Lo
is shunted by a fixed condenser of 40 micromicrofarads (40mmf.) value.
Before closing the discussion, we must include a few words on the antenna coupling,
and see how much voltage stepup we can expect in this tuned circuit. The constants
which have been assumed, in making the calculations for the preceding curves, are
those shown in the curves of Fig. 9; which are experimental values taken on
a regular commercial R.F. transformer. In making the calculations for the antenna
circuit the constants shown on the curve were assumed. Two curves are shown; one
of these is for a fairly large coupling and a fairly large antenna; the second is
for a smaller antenna and looser coupling. In the lower curve these values have
been reduced, in order to see how much the amplification is lowered. As these curves
show, we can expect the voltage amplification in the antenna coupling transformer
to vary from perhaps unity to as much as 30. This effect also contributes considerably
toward making the amplification characteristic of the entire amplifier quite steep
with regard to frequency; and it must be compensated for by the special transformer
primaries.
Selectivity Found in Number of Circuits
Before closing it will be well to include a few remarks about the selectivity
to be expected from such circuits. Fig. 10 shows curves which have been calculated
for the two circuits  the interstage circuit and the antenna circuit. It will be
seen that there is not a great difference between the selectivities of the two circuits,
although the antenna circuit is somewhat less sharp in tuning than the interstage
circuit; which we may well expect, considering the resistance of the antenna. In
the interstage coupling the primary resistance (the plate resistance of the tube)
is so great that the primary has little effect on the tuning of the secondary and
on its selectivity.
Although these curves may seem to be quite broad, upon first inspection, it must
be remembered that the great selectivity of an amplifier is dependent mainly upon
the number of tuned circuits, and not upon the selectivity of each single circuit.
By this we mean that only small improvements in overall selectivity can be made
by improving the selectivity of the individual stage; practical, commercial tuned
circuits are about as selective as we can make them without adding considerably
to the cost. Great improvement in selectivity may be obtained by adding a special
tuned circuit to the amplifier; whereas, a slight improvement in the selectivities
of the several tuned circuits (as by reducing their losses), will hardly result
in any improvement that might be considered appreciable.
Posted June 28, 2024 (updated from original post
on 12/22/2016)
