April 1932 Radio-Craft
Wax nostalgic about and learn from the history of early electronics.
See articles from Radio-Craft,
published 1929 - 1953. All copyrights are hereby acknowledged.
The use of intermediate frequency (IF) coils and interstage
coupling transformers were a major feature of vacuum tube based
receivers. Both served the dual purpose of impedance matching
and frequency selectivity. Resistive losses in the relatively
large passive components required careful attention to matters
that affect signal sensitivity, especially in the front end
where losses add significantly to the overall noise figure.
This article appeared in an early 1930s edition of Radio-Craft
magazine at a time when
superheterodyne receivers were just coming into popularity
and were a new challenge for many designers.
I.F. Coil & Transformer Design
The "how" and "why" of intermediate-frequency transformer
By Clifford E. Denton
The increasing interest in superheterodyne receiving circuits
from the home constructors' and experimenters' angle has made
more plaintive than ever that old refrain - "How many turns
should I wind on an intermediate-frequency transformer?"
Fig. 1 - Elementary circuit of a typical
The author will endeavor to supply such information as is
necessary to enable the builder to design and construct coils
which will be as good as, if not superior to, any on the market.
A discussion of the advantages of a particular frequency,
such as 175 kc., over that of, say, 45 kc., is not within the
province of this article. There are many reasons set forth by
engineers as to the respective merits of the various intermediate
frequencies of their choice, but today we find that for ordinary
broadcast reception the 175-kc. band has become more or less
standard. For short-wave "superhets," other frequencies (some
within the broadcast band) are used; so the tables which are
given in this article, for those who are not so mathematically
inclined, include all frequencies from about the center of the
broadcast band to the old stand-by frequency, 45 kc.
Three of the most important factors to be taken into consideration
in the design of I.F. transformers are:
1. The sensitivity required to obtain the required power
output from low signal inputs;
2. The degree of selectivity necessary per stage to give
a satisfactory over-all selectivity in the receiver; and
3. Mechanical and cost considerations such as chassis size,
coil-shield size, number of tubes, etc.
An examination of the factors listed above will lead us to
believe that there is more to the design of an I.F. transformer
than the mere selection of a coil with a given diameter and
wire turns plus a resonating capacity.
The logical way to design our coils is, first, to determine
the required degree of sensitivity. If we know the total over-all
gain required for a given output, we can ascertain the required
gain per stage. We shall have a fair idea of the grid
swings on successive stages at full power output, which will
enable us to design our circuits for minimum tube distortion
and maximum selectivity and stability. The solution of the 1st
factor listed will be a guidepost in the determination of factors
2 and 3.
Fig. 2, left - Curves showing the possible
gain that may be expected from a '24 tube.
Fig. 3, center
- The same curves as in Fig. 2, only for a '27.
right - Same as for Figs. 2 and 3 but for a '32.
Instead of using the level of 50 milliwatts output, we shall
use the rated power output of the tube or tubes as indicated
in the various tables supplied by tube manufacturers.
If the power tube selected is of the '45 type, the power
output will be 1600 milliwatts at the maximum rated voltage.
This means that if we want a power output of 1.6 watts (1600
milliwatts) to be fed into the speaker, the input signal voltage
on the grid of the '45 must not be greater than 50 volts peak
(the value of the grid bias).
Any increase of voltage on the grid will be the cause of
undesirable distortion and, of course, must be avoided. It is
best to use R.M.S. values in calculating the various signal
voltages, and as the R.M.S. voltage of 50 V. is 0.707 x 50 =
35.35 volts, we find that the R.M.S. value which can be applied
to the grid of the '45 is 35.35 volts.·
Most radio sets today feed the audio output of the detector
into the grid of the power tube by means of resistance coupling;
in this case, the detector will have to deliver 35.3 volts to
the grid of the output tube.
Figure 1 shows the circuit of a power detector, resistance-capacity
coupled to the output tube, and we find that in the case of
a screen-grid detector and a '45, E3 will be 35.35 RM.S. volts.
No gain can be expected from the resistance-capacity unit so
that the voltage at E2 must also be 35.35 volts. Figs. 2, 3,
and 4 show the possible audio output of three standard tubes
used as second-detectors in "superhets." These curves show the
A.F. output volts (R.M.S.) of the '24, '27, and '32 tubes plotted
against the R.F. input volts (R.M.S.) and are very useful in
view of the fact that they give us the required operating potentials
for these tubes used as detectors and the required H.M.S. values
of the incoming signals to '''kick'' the power tube. Figs. 2
and 3 also show the points where grid current will start due
to overloading of the grid by the incoming signals.
Fig. 6, upper right - Circuits illustrating
the effects of distributed capacity.
Fig. 7, lower right
- Circuit illustrating the effects of coil resistance on a tuned
Fig. 8, left- Curve showing how the "Q" of
a coil may be computed.
Referring to Fig. 2, we find that a signal of 3.24 (R.M.S.)
volts is necessary on the grid of the '24 detector to fulfill
the requirements of the '45 for maximum power output. The signal
on the grid should not exceed 4 volts R.M.S. or the grid will
draw current, thus causing distortion. In the case of the '27,
Fig. 3, we find that it would require all R.F. input of 12 volts
to deliver an A.F. output of 13 volts, This tube will not satisfy
the condition of maximum power output unless a high-primary-inductance
A.F. transformer, with a turns ratio of at least 3.5 to 1, is
used. A bad feature of such a tube is the fact that grid current
starts to flow at about 12.5 to 13 (R.M.S.) R.F. volts. Under
all conditions, it is advisable to work the tube at some value
below that which causes the flow of grid current.
If it is desired to use a pentode as the output tube with
a screen-grid second-detector, we find that an R.F. signal input
of less than 2 volts will be sufficient to deliver a power output
of 2.5 watts.
If push-pull circuits are used in the output stages, the
A.F. signal voltages will have to be doubled and, as the output
of the detector cannot be increased without severe distortion,
it is necessary to add an additional A.F. stage so as not to
overload the detector.
Fig. 5 - An elementary circuit illustrating
how a signal is amplified through an amplifier.
Calculation of Gain
Having determined the minimum R.F. voltages which must be
supplied to the grid of the detector to deliver the maximum
power output, we are in a position to determine the total gain
which must be obtained from the I.F. amplifier.
Modern radio receivers of the super-heterodyne type have
an input sensitivity of less than 5 microvolts per meter and,
with the standard height of the antenna set at 4 meters, we
find that the absolute sensitivity will be about 20 microvolts
(a microvolt being one-millionth of a volt). Thus, if we desire
a receiver (as shown in Fig. 1) that will deliver about 4 volts
of R.F. signal to the detector from an input signal of 20 microvolts,
the total voltage gain of the amplifier will be
As a certain amount of amplification can be, and is, obtained
by one or more stages of conventional T.R.F. ahead of the modulator
tube (first-detector), it is not absolutely necessary that the
entire burden of amplification be borne by the I.F. amplifier.
If there are two stages of T.R.F. ahead of the modulator, then
there will be a voltage gain of about 1500 (assuming a gain
of about 40 volts per stage) which must be considered in designing
the I.F. amplifier. The reader will recognize the necessity
of using pre-amplification before the modulator as this phase
has been covered in many excellent articles on the subject.
Now, let us see just what the final figures will be with
the added gain obtained in the pre-amplifier.
If the input to the receiver is 0.00002-volt and the pre-amplifier
has a gain of 1500, then the input to the first I.F. transformer
will be 0.00002 x 1500 or 0.03-volt. The 4 volts required by
the detector, divided by the 0.03-volt input to the I.F. amplifier,
will then be the voltage gain required by the I.F. amplifier,
which is 133.3 volts. The input to the receiver is 0.00002-volt
and the pre-amplifier has a gain of 1500, then the input to
the first I.F. transformer will be 0.00002 x 1500 or 0.03-volt.
The 4 volts required by the detector, divided by the 0.03-volt
input to the I.F. amplifier, will then be the voltage gain required
by the I.F. amplifier, which is 133.3 volts.
As it will he impossible to obtain a gain of 133.3 in a single
intermediate stage, .it will be necessary to use two stages
working at a gain of about 65, or three working at 44 per stage.
In the example cited above, the amplification due to the
modulating tube is ignored, as various conditions develop which
cause the gain of this portion of the circuit to vary over wide
ranges. The sensitivity and output will be affected by the strength
of the received signal, by the power output of the local oscillator,
and by any change in operating potentials which may take place
as the receiver is functioning.
The check for the correctness of the calculation can be made
by multiplying the gain in the pre-amplifier by the gain in
the I.F. amplifier; thus, 1,500 x 133.3 gives a value of 199,950.
Figure 5 shows a skeleton circuit with the voltages developed
in the various circuits. Two stages of I.F. amplification are
shown and, as each stage is not working at the maximum possible
gain, the I.F. amplifier will be very stable and the coils easy
Fig. 9 - An automatic coil-condenser calculator.
Knowing the value of either a coil or a tuning condenser, the
other may be determined, for any wavelength by reference to
If an actual condition exists where the gains and voltages
are measured and found to be as indicated in Fig. 5, the volume
control on the pre-amplifier end of the receiver will be full
on and the gain on the I.F. amplifier cut away down.
If the pre-modulator amplifier is limited to one stage, it
will be necessary to increase the gain of the I.F. amplifier
if the same level of sensitivity is to be maintained.
Unlike the conditions which exist in T.R.F. amplifiers (where
the limitations of the minimum and maximum capacity, range of
the tuning condenser, plus the unavoidable circuit capacities,
define the maximum ratio of the tuning inductance to its tuning
capacity), we find that the tuning circuits of I.F. amplifiers
are not limited as stated above, and the ratio of L to C can
be any ratio desired, within sensible limits.
Table I - Turns-Per-Inch of Insulated Wire
Thus, the inductance of the I.F. transformer can be made
as large as desired; the limitations being defined by the R.F.
resistance and the physical size of the coil and associated
shield. As the frequency of the I.F. amplifier is generally
lower than the broadcast-band frequencies, the effect of the
circuit and coil capacities can be neglected for the moment
as any calculation which we shall make will generally assume
that the signal is fed into the tuned circuit by induction in
the coil itself. In Fig. 6A, we find that the distributed capacity
of the coil shunts the tuning condenser and is simply added
to the circuit r in Fig. 6B, the signal is in series with the
Calculation of Load Impedance
To obtain the greatest percentage of the "mu" of a vacuum
tube, it is necessary that the load in the plate circuit be
as large as possible.
The effective impedance of the tuned circuit at resonance
(Fig. 7) is equal to
where L = the inductance of the coil,
W = 6.28 times the frequency f,
r = the series high resistance of the coil,
C = the capacity necessary for resonance.
It will be noted that the effective impedance increases as
the square .of the inductance; so, provided we keep the R.F.
resistance of the coil low, a large inductance will be superior
to a small one.
In such a tuned circuit, the selectivity S will be proportional
and the width of the resonance curve, Fig. 8, at a point
where the response is 0.707 times the value at resonance, is
related to the ratio
giving another valid reason for using a coil as large as
possible. A handy rule to use in the design of such circuits
should be less than 250, for if the ratio of the inductive
reactance of the coil to the R.F. resistance is greater than
250, there will be marked attenuation of the higher audio frequencies
in the detector output.
The condition of resonance is the same, no matter what the
frequency may be, and the old L.C. chart is as useful as ever;
as it gives the L.C. constants for all frequencies between 1000
and 42 kc., thus taking in all of the frequencies used in I.F.
Design of an I.F. Transformer
Most of the readers will be interested in 175-kc. intermediates,
so a design will be developed for this frequency.
Examination of such a chart shows that 176.5 kc. is the nearest
frequency to 175 kc. and will be satisfactory for our purpose.
The L.C. constant for this frequency is 813 when the inductance
and capacity are expressed in centimeters (1000 centimeters
equal one microhenry) and microfarads, respectively.
The Radio-Craft readers, who have followed the articles by
this author on the calculation of R.F. coils in previous issues,
will be familiar with the method involved in determining the
values of the inductance and capacity by the process of dividing
one known value, either L or C, into the L.C. constant to derive
There are several types of semi variable condensers with
capacity ranges running up to 140 mmf., which could be shunted
with a good grade of fixed condenser to increase the maximum
value of capacity if desired. Earlier; we discussed the added
gain to be obtained by the use of a large inductance provided
the R.F. losses of the large coil did not affect the resultant
amplification and selectivity.
Table II - Winding data for three types of
So, for the tuning: capacity, let us select a unit with a
maximum capacity of 140 mmf. and see just what inductance will
be necessary to tune to 176.5 kc. As
and as 1000 centimeters equal one microhenry, we require
an inductance of 5,800 microhenries. Now 5,800 microhenries
is considerable inductance to put in a small space, but a good
coil can be had by using any of the commonly-known methods of
winding, such as diamond weave, duo-lateral, honeycomb, etc.
Most of us do not have the equipment on hand to wind a coil
in this manner, so it would be practical for us to increase
the size of the tuning condenser to 0.0005-mf. so that we could
reduce the inductance to a lower value. Semivariable condensers
of compact size can be obtained in ranges up to 0.001-mf. and
are satisfactory for I.F. circuits. With the new capacity of
0.0005-mf., we find
By reference to the chart in Fig. 9, we can determine a coil
which can be hand wound at home.
By connecting three known or assumed values as per the key,
we find that a coil wound on a 2-in. diameter cylinder 3 ins.
long, having 120 turns per in. for a length of 2 ins., or a
total of 240 turns of No. 34 S.S.C. wire, will have an inductance
of 1,625 millihenries. A coil made up in this size can be placed
in a shield, providing that the distance from the coil to the
shield is at least 1 1/2 ins. all around. Under these conditions,
it will be necessary to add 20% to the inductance of the coil
to compensate for the loss due to the effect of the shield.
A wire table is given in Table II for the convenience of
the reader and takes in all of the commonly-used sizes and coverings.
The impedance of the combination is equal to
The resistance r is assumed to have a value of 32 ohms.
Selecting the Circuit
Fig. 10 - At A, B, C, D, E, and F are shown
the various methods of coupling I.F. amplifiers.
With the solution of the effective impedance of the tuned
circuit at the resonant frequency, we can select the circuit
in which the coil and condenser are to be used. Fig. 10 gives
several possible variations, all incorporating the tuned circuit
with its impedance of 100,000 ohms at 175 kc. A in Fig. 10 is
the old tuned-plate type of R.F. circuit and, if used with tubes
whose internal impedances (Rp) a re less than 100,000
ohms, will not tune sharply. B in Fig. 10 has a primary design
to match the tube Rp if possible and has a definite
voltage gain when used with low-impedance tubes. The circuit
in C, Fig. 10, is not used as the losses due to the shunting
effect of R1 and R2 reduce the effective load in the plate and
will not be selective. In D, Fig. 10, the plate circuit is loaded
by the choke R.F.C. and the signal is passed to the tuned circuit
through the coupling capacity. A circuit which is used in A.K.
superheterodynes is shown at E, Fig. 10. Here two tuned circuits
are used to increase selectivity.
Most I.F. amplifiers today have tuned input and output circuits
as shown in F, Fig. 10. Both coils and condensers are tuned
to the same frequency and the mutual inductance between the
coils is held to a low value. In some cases, the circuits are
detuned, thus causing a flattening out of the peak of the resonance
curve shown in Fig. 8.
The following table contains practical values for the turns
ratio of the windings used in circuit B, Fig. 10. These ratios
are not the maximum but are good workable ones giving excellent
gain, good selectivity and stability.
Transformer data for circuit B. Fig. 10.
The standard form used for winding any of . the above is
3 ins, long and 2 ins. in diameter.
This article is based on the reference material gathered
by the author over an extended period of time and he hopes that
it will prove as useful to others as it has to himself in the
Posted July 20, 2015