April 1932 Radio-Craft
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 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?"
Fig. 1 - Elementary circuit of a typical I.F. amplifier.
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.
Design Considerations
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.
Fig. 4, 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.
Preliminary Calculations
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 circuit.
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 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.
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
Inductance Design
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 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 to
S =
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.
Table II - Winding data for three types of coils.
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
1,626 microhenries.
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 past.