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
receivers were just coming into popularity and were a new challenge for many designers
because of the variable frequency oscillator.
I.F. Coil & Transformer Design
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 circuit.
Fig. 8, left- Curve showing
how the "Q" of a coil may be computed.
The "how" and "why" of intermediate-frequency transformer construction
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?"
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
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.
Fig. 1 - Elementary circuit of a typical I.F. amplifier.
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.
Fig. 4, right - Same as for Figs. 2 and 3 but for a '32.
Fig. 5 - An elementary circuit illustrating how a signal
is amplified through an amplifier.
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.
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
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
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.
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.
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 to design.
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 the chart.
Table I - Turns-Per-Inch of Insulated Wire
Table II - Winding data for three types of coils.
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
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
Thus, the inductance of the I.F. trans-former 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 coil.
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
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 to
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 is that
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. amplifier design.
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 the other.
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.
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.
Fig. 10 - At A, B, C, D, E, and F are shown the various
methods of coupling I.F. amplifiers.
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
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.
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 past.
Posted February 17, 2023
(updated from original
post on 7/20/2015)