Quick Summary:  A device is described that works the same as an audio transformer when connected between the output of a diode detector and headphones, but it has several differences.  (1) No power loss.  (2) Input and output resistances can be varied over a wide range by selector switches.  Its purpose is to enable experimentation to determine the optimum impedance transformation for a real world transformer when experimenting with different diodes and headphones.  It also has a switcheable 20 dB amplifier to enable better reading of very weak signals. 
 

• 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 if the optimum diode load resistance changes from one end of the BC band to the other by adjusting SW3.  It usually does change.
• Some of the mystery can be taken out evaluating diodes for weak signal reception.  A diode will exhibit its greatest weak-signal sensitivity when the RF source resistance driving it and its audio load resistance are equal. (See Article #15 for an exception to this, applicable to weak signal reception.)  If they are not equal, its greatest weak-signal sensitivity will occur when the product of the source resistance and diode load resistance is equal to Ro^2.  Here, Ro is defined as the slope of the V/I curve of the diode at its axis crossing.  The numerical value of this resistance using SPICE parameters is: Ro=((T+273)*n)/(11600*Is).  T=temperature in degrees C.  Is=Diode saturation current.  n=Diode ideality coefficient.  See Articles #0 and 1 for more info on this.  Is and n for Schottky diodes are usually available from their Spec. Sheets.  The values for Germanium diodes must be obtained from measurement.  A diode detector will exhibit poor weak signal sensitivity when used in a circuit having RF source and audio load resistances differing greatly from the Ro of the diode.  When comparing various diodes in a crystal set that is using a Unilateral 'Ideal Transformer' Simulator (UITS), the optimum audio load resistance for that diode can be easily dialled 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).
• 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.  A side benefit is that the best setting of SW4 indicates the average impedance of the headphones.  For more info on this, see Articles #2 and 3.
• An added feature of the device as implemented here 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 +/- 0.1 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 loss (or gain), no matter what 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 exclusive 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.

One of the problems one encounters when designing a high performance crystal 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 is 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 its crystal set application.

Consider the performance of two transformers having the same transformation ratio, but 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-157, PT-156, Stancor A-53C or similar transformer originally designed to couple the output of a first 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 380,000 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 equivalent 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 equivalent 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 will 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 get 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.
 
 

How should one proceed in determining the Specifications for a transformer that will provide optimum performance in the crystal 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 since the device is unilateral. The equivalent 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 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.

Note. The parallel RC (see Article #5) needed in series with the primary of an actual transformer is not needed with the UITS because its input resistance is the same for DC as AC.
 

Fig. 1

Fig. 2

Some component specifics: 

• B: 9 Volt batteries.
• IC: JFET input op-amp such as one section of an LF353 or M34002.  Basically, it should have a JFET input and a gain-bandwidth product of about 4 MHz.
• The 22 uF electrolytic caps should have a voltage rating between 10 to 25 Volts.
• The 10 uF caps can have a voltage rating of 5-10 volts

Calibration is simple. Set SW2 to the 0 dB position, SW3 and SW4 to their 10k Ohm settings and 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 voltage at J1.  Use an audio generator and DVM to read the voltage at P.  If no audio generator is available, connect the output of the crystal set diode detector (no audio transformer used) to J1 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 set detector to the ITS 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 bypass capacitor or an interconnecting cable of too high a shunt capacity for the resistance setting of SW3.  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.

 Published: 01/05/01;  Last revision: 04/14/01

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