No-loss audio transformer simulator with independently adjustable input and output impedances

Quick Summary: This device works as an audio transformer when connected between the output of a diode detector and headphones, but with several differences. (1) No insertion power loss. (2) Input and output resistances can be independently varied over a wide range by selector switches. This provides for the simulation of a wide range of "transformer turns ratios".

The main purpose of this device is to enable oneself, by twisting two dials, to find out the optimum audio impedance transformation needed in a 'real world transformer', while experimentally trying different diodes or headphones in a crystal radio set. The effect the transformer has on selectivity and volume may be evaluated. Another purpose is to enable one to check how closely the performance of one's audio transformer conforms to that of an ideal one, both having the same input and output impedances. It also has a switchable 20 dB amplifier to enable better reading of very weak signals.

The first version of this device, shown in Figs. 1, 2 and 3 is designed for driving typical sound-powered balanced-armature, magnetic diaphragm or piezo electric earphones. The schematic for Version B, shown in Fig.4 is designed for feeding a wider range of loads, down to an impedance of 8 ohms. This unit can match the impedance of the earphones mentioned above as well as that of typical dynamic earphones.

Consider a crystal radio set that uses an audio transformer to drive headphones. One can determine what its performance would be if the transformer had no loss and provided an optimum impedance match between the output resistance of the diode detector and the headphone load.

One can determine if the optimum diode load resistance changes as a function of signal level by adjusting SW3 for the loudest volume on a weak signal and then readjusting it for a strong one.

One can determine the optimum turns ratio for a real-world transformer. To do this, set SW3 and SW4 for maximum volume. Calculate the output-to-input winding turns ratio as the square root of the ratio of the port resistances of SW4 to SW3 (the numbers in parentheses in Fig. 3).
One can determine if the optimum diode load resistance changes from one end of the BC band to the other by adjusting SW3. It usually does change, when receiving strong signals.
Some of the mystery can be taken out of evaluating diodes. A diode will exhibit its best weak-signal sensitivity when the RF source resistance driving it, and the audio load resistance are set to the optimum values for that diode. When comparing various diodes in a crystal radio set that is using a Unilateral 'Ideal Transformer' Simulator (UITS), the optimum audio load resistance required for that diode can be easily dialed up just by setting SW3 for the loudest volume. The diode is then not penalized for being used in a poor impedance environment (for that diode).
The sensitivity of various headphones may be compared without the problem of needing an optimum audio transformer for each. Just adjust SW4 for maximum volume on each headphone and read the approximate optimum source resistance from the calibration.
One can determine, in a particular crystal radio set, how closely a particular real-world transformer emulates an ideal one.
One can easily demonstrate how the frequency response (tone quality) of a particular headphone changes as a function of the source resistance driving it by changing the setting of SW4.
One can also find out out if one's real-world audio transformer alters tone quality. This can happen if its shunt inductance is too low or if its distributed winding capacitance is too high.
The average audio impedance of headphones can be determined. For more info on this, see Articles #2 and 3.
An added feature of the device as implemented is the capability of adding a 20 dB boost to the audio signal (this is where the plus... comes from). This feature does not affect the input and output resistances. It can be used to just add volume to weak signals, or as an aid in centering tuning on a very weak signal.
In normal operation (20dB boost turned off), the UITS is calibrated to provide no power gain of loss. It has a flat frequency response +/- 0.3 dB over the audio band of DC - 3.3 kHz.

The UITS, unlike a real world transformer, can pass a signal from the input port (J1) to the output port (J2), but not from J2 back to J1. The 'unilateral' in the name comes from this property. See Fig. 3. A real world transformer is bilateral. That is, it can pass a signal in either direction.
A good transformer has very little loss. The UITS can be set to have no power loss (or gain), no matter what the effective turns ratio setting is. The effective turns ratio is controlled by the settings of SW3 and SW4. A real world transformer has a turns ratio of, say 'n'. This gives it an impedance transformation ratio of n^2. That is, a resistor of value R, connected to one winding will be reflected as a value R*(n^2) or R/(n^2) at the other. 'n' is a fixed parameter of the real world transformer unless it has taps, then several various values of 'n' can be obtained. The UITS can be adjusted with SW3 and SW4 to a very wide range of transformation ratios. It has the advantage of independent control of input and output resistance by means of switches, with no power loss for any combination of input and output resistance.

3. A Short tutorial on some aspects of audio transformer utilization in crystal sets.

One of the issues one encounters when designing a high performance crystal radio set is determining the optimum parameters for the detector-to-headphone audio coupling transformer. Its impedance transformation ratio is the main factor to be considered, though the inherent loss and reactance parameters are also important. Another factor is the primary and secondary impedance levels for which the transformer was designed, compared with the levels to be used in a crystal radio set application.

Consider the performance of two transformers having the same transformation ratio, but originally designed to operate at different impedance levels. They will not perform the same. To illustrate this point we will consider a transformer designed to transform a 10,000 Ohm source to a 90,000 Ohm load. This could be an AES PT-156, Stancor A-53C or similar transformer originally designed to couple the output of a first (tube) audio stage to push-pull grids. If the designer did a good job, this transformer will have the lowest possible loss consistent with its specified frequency range, power handling capability and cost goals. If it were to be driven from a 40,000 Ohm source and loaded with a 360,000 Ohm load (still a 1:9 impedance ratio), its center-band power insertion loss will be increased and the low frequency end of the band will be rolled off. The reason for the increase of center-band loss is that the shunt resistance caused by losses in the iron core load down the now higher source resistance (40,000 Ohms) thus increasing loss. The shunt inductive reactance of the primary winding, at the low end of the band loads down the now higher source resistance (40,000 Ohms) more than before, thus increasing the roll-off at the low frequency end of the audio band. The high end of the audio band will also probably be rolled off because the reactance of the shunt capacitance of the primary winding will cause more loss when being driven by a 40,000 Ohm source than one of 10,000 Ohms. On the other hand, if the transformer was driven from a 2,500 Ohm source and fed a 22,500 Ohm load, center-band power insertion loss again still be increased. The reason is the ratio of the source resistance to the series resistance of the primary winding is not as high as when the source was 10,000 Ohms. More of the input power will be dissipated in this series resistance and less transferred to the secondary. A similar loss effect from the winding resistance occurs in the secondary. The low frequency end of the band will reach to lower frequencies than before, but the high end may get some roll-off due to leakage inductance in the primary and secondary windings. One can think of this effect by visualizing a parasitic inductor in series with the primary and secondary windings.

It is important to understand that the impedance numbers a transformer manufacturer specifies for various terminals are the source and load resistances they used to specify the performance of the transformer. In most instances when one uses a transformer originally designed for use between tubes (plate-to-grid) or to match a low impedance line to a plate or grid in a high-performance crystal set application, the following statement applies: Optimal results usually occur when the actual crystal set source and load resistances are higher than the values for which the transformer was designed, but are of the desired ratio. For instance, if a Stancor A-27 transformer is connected with terminals 8 and 9 joined together and 3 and 4 joined together (diode input to pin 7, diode return to pin 10), it is specified by the manufacturer for use between a 100k source and 600 ohm load connected to pins 1 and 6. Using it between approximately 200k and 1.2k ohms will result with a very slight increase of midband transformer power loss, but a greater offsetting increase of detector sensitivity from the higher detector load of 200k. This assumes a diode having a relatively low saturation current such as a Schottky, FO-215 or other high axis-crossing-resistance diode is used. The audio bandwidth will also be reduced but probably by a non-perceivable amount. Some illustrations of these effects can be viewed in Article #5, Tables 5, 7 and 8. To go further in this direction to present the diode with an even higher transformed resistance from a 1200 ohm load, connect the load to terminals 1 and 5 instead of 1 and 6. Volume may diminish from increased transformer loss and reduced audio bandwidth.

How should one proceed in determining the specifications for a transformer that will provide optimum performance in the crystal radio set? One may not know the audio source resistance of the diode detector, or even the average impedance of the headphones load. The UITS can be used to find these two values. It also has a 20 dB gain switch option that can be used to enable reception of very weak signals as well as a switch to block DC from the phones, if desired. There are two operating adjustments. One sets the input resistance Ri, the other the output resistance Ro. These two settings don't interact. The equivalent real-world transformer turns ratio is the square root of the ratio of the two resistance settings. Here are some ways that the UITS can be used:

Compare the performance of a candidate transformer to that of an ideal transformer to see how much signal is lost in the candidate. There is no point in looking for a better transformer if the difference between the two is small.
Use it to find the impedance transformation ratio that would be optimum for the crystal radio set/headphone combination being used.
Use it in place of an actual transformer.
Enhance reception of very weak signals.
See bullets in the "What's it good for?" section, above.

To use the UITS, connect it between the detector output and headphones. Insure that the diode has an appropriate RF bypass capacitor. Set the amplification to 0 dB. Adjust each rotary switch independently for the loudest volume. Calculate the impedance transformation ratio from the settings of S3 and S4. A transformer specified with this ratio is optimum for the detector and headphone impedances being used, all other things being equal. Its specifications should include primary and secondary source and load resistances about equal to the values determined with the UITS. A transformer that has factory specified impedance levels as much as four times lower than desired, but with the correct transformation ratio, and a frequency response range much wider than 0.3-3.3 kHz will probably work well.

Note. The parallel RC (a 'benny') (see Article #5), needed in series with the primary of a real world transformer, is not needed with the UITS because its input resistance is the same for DC as for AC.

B: 9 Volt batteries.
IC: JFET input op-amp such as one section of an LF353, TL081 or M34002. Basically, it should have a JFET input and a gain-bandwidth product of 3 MHz or more.
The 22 uF caps, electrolytic or tantalum, should have a voltage rating between 10 to 25 Volts.
The resistor values shown in the schematic are those in the standard 5% series of values. The use of resistors that difer by +/- 10% from the values shown should not have an appreciable impact on performance of this unit.

Calibration is simple. With SW2 in its 0 dB position and SW3 and SW4 at their 10k Ohm settings, set potentiometer P for zero gain. To do this, load J2 with a 10k Ohm resistor and feed a 1 kHz signal from an audio generator into J1. Adjust P so that the output voltage at J2 equals the input voltage at J1. If no audio generator is available, connect the output of the crystal radio set diode detector to J1 (no audio transformer to be used), and a headphone set of about 10k ohm impedance (2k ohm DC resistance) to J2. Tune in a station and adjust potentiometer P so that the volume is the same as when the detector output feeds the headphones directly. This setting does not have to be changed in the future. Note: Connect the output of the crystal radio set detector to the UITS with as short a length of cable as possible in order to minimize added shunt capacity. If the tone quality of the signal changes from one resistance setting of SW3 to another, the shunt capacity in the detector output circuit is too high. This can be caused by using a diode RF bypass capacitor or an interconnecting cable of too high a shunt capacitance for the resistance setting of SW3 being used. I use an eighteen inch length of RG-59 type coax for my cable. It has a capacitance of about 20 pF per foot.

The performance of magnetic diaphragm type headphones can be affected by the DC current passing through them when no coupling transformer is used. SW5 is provided for those who choose to block the DC.

6. Schematic for version B (Added 05/25/2003). The differences between this version and that shown in Fig. 3 are:

A Zero Loss, Unilateral 'Ideal' Audio Transformer Simulator, plus... This device makes is very easy to determine the optimum audio transformer source and load resistances for any crystal set diode/headphone combination. No test equipment necessary