Audio transformer power loss and optimal impedance matching

Quick Summary: This Article discusses the use of audio transformers with crystal radio sets and gives the results of loss measurements on several of them. A method for measuring insertion power loss is also described.

Many crystal radio set designs provide impedance step down taps on the final RF tuned circuit. If the diode is connected to one of these taps, its loading on the tuned circuit is reduced and selectivity is improved. Too much of a step down also reduces sensitivity. RF tuned circuit loading by the diode is affected by the diodes' Saturation Current, the headphone effective impedance and the signal level. One can reduce the loading effect of headphone effective impedance and of high signal level by transforming the headphone impedance up to a value that matches the audio output resistance of the diode detector itself. This approach can keep the selectivity high and also increase the sensitivity of the crystal radio set. For info on measuring headphone effective impedance see article # 2.

It is important that the diode sees a DC load equal to its AC audio load. This will permit connecting the diode to a higher tap or maybe to the top of the tuned circuit. The result will be to maintain selectivity and reduce audio distortion for medium and especially for strong signals. Diodes of lower Saturation Current can be tapped up higher on the tuned circuit than those of higher Saturation Current and, all else being equal, will give higher receiver sensitivity. See articles #0, #1, #4 and #15.

Part 1 - Setup for switchable Transformation Ratios using the A.E.S. P-T157
or equivalent transformers

The sensitivity improvement mentioned above will only be attained if the audio transformation is performed with a low insertion loss audio transformer. For experimental purposes one of the best transformers I have found is the P-T157 from Antique Electronic Supply. What immediately follows is the description of two switchable circuits that can supply various transformation ratios for driving a 12k Ohm load. This is the nominal AC impedance of most 2,000 DC Ohm headphones, as well as many piezoelectric ceramic earpieces. Later on, specific non-switched configurations are shown for several different transformers. Since this Article was written, A.E.S. has stopped selling the P-T157. Results close to those shown below can be obtained using the A.E.S. P-T156, Stancor A-53 or most any 3:1 turns ratio tube-type inter-stage audio coupling transformer. A good description of this type of transformer is: A transformer designed for plate-to-grid inter-stage coupling, having a 3:1 turns ratio, and specified for a 90k to 10k ohm impedance transformation. Henceforth, in this Article, this type of transformer will be referred to as a "3:1 AIT".

Note that the switched transformation ratios shown below vary by a factor of about four from one to another. Note also that an impedance mismatch of 2:1 gives an insertion loss of only 0.5 dB. This means that all values of diode output resistance from 12k Ohms up to 750k can be utilized, with a mismatch insertion loss of no more than a maximum value of 0.5 dB, plus the transformer loss. Measured transformer loss is about 1.0 +/- 0.5 dB from 300- 3300 Hz at the 63 times ratio and about 0.5 +/- 0.2 dB at the 16 and 4 ratios. Note: The transformation ratio on the H switch position is shown as 63 instead of 72 because of shunt resistive losses in the transformers. On this switch position the diode sees the 12k headphones transformed to 750k, not 860k. T1 and T2 are preferably Antique Electronic Supply P-T157 transformers. Alternatively, one can use most any generic "3:1 AIT". One will get a small amount more loss with the alternatives, mainly at 300 Hz and when the signal is weak. C2 can be used to peak up response at 300 Hz if a generic "3:1 AIT" transformer is used. C2 can be omitted if the P-T157 transformers are used. Experiment with values around 0.02 uF. Sw1 and Sw2 are DPDT slide or toggle switches. R can be a 1 Meg pot. It is used to set the diode DC load resistance to be equal the transformed AC load impedance.* A log taper is preferred. Set R for the lowest audio distortion and best selectivity on strong signals. The diode load at DC must be the same as for AC audio signals for best results. This setting has little effect with weak signals, however. C1 should be about 0.05 uF. See the later part of Article #1 for info on determining transformer winding polarity and how to reduce the effect of inter-winding capacitance.
* The first time anyone has suggested placing a parallel RC in series with the diode to enable adjusting its DC load resistance equal its average AC load may have been in Article #1. Some people call it a "benny".

There is no need to transform headphone effective impedance up to as high as 750k unless the RF tuned circuit, when loaded with the antenna, has a resonant resistance of around 750k Ohms. It is very difficult to attain an impedance this high. The diode also would have to have the appropriate Saturation Current of about 38 nA. For experimental purposes, if a transformed impedance of no higher than 380k is desired, a one transformer circuit should be used as shown below. This will prove more practical in real world applications. R may be a 250k or 500k Ohm pot, preferably with a log taper. The transformer insertion loss remains below 1.0 dB from 0.3-3.3 kHz with output loads between from 6k to 24k Ohms when using the A.E.S. P-T157. Keep in mind that the saturation Current (Is) of the diode should be such that the diode's (Weak signal) RF input resistance is about equal to the (Antenna loaded) RF tuned circuit resonant resistance and also to the transformed headphone effective impedance. This diode resistance is equal to (0.0257*n)/Is. Is is in Amps. For more information on this, see article #4 listed on the home page.

The following schematics show various connections for the transformers mentioned above. The connections are arranged to provide various diode audio frequency load impedances from headphone loads of either 12,000 or 1,200 Ohms AC impedance. The 12,000 Ohm connection is appropriate for most magnetic headphones of 2,000 Ohms DC resistance and many piezo earpieces. The 1,200 Ohm connection is used when driving a series connected set of typical sound powered elements.

As stated before, it is important that the diode have a DC load of the same value as its average AC load. This can easily be accomplished by placing the parallel combination of a pot with an audio bypass capacitor (a "benny") in series with the lead marked 'RC' between the points marked "x--x" (see below). The pot should have an audio taper and be connected as a rheostat. 0.5 to 1 Meg is usually a good value. The value of the capacitor depends upon the impedance reflected into the transformer primary from the headphones. A value of 0.05 uF or more is usually OK. The pot should be adjusted to minimize distortion and improve selectivity when receiving strong signals. Its setting has no effect when receiving weak signals.

First, some help. In schematics A-F it is important to properly phase the windings. For best performance at the high end of the audio band, one should minimize the effect of transformer inter-winding capacitance. This is most important to do when using circuits D or E, but has little effect when using circuits A, B, C, or F. To do this, the start and finish leads of the transformer coils must be properly connected. In the schematics shown above, the start and finish of the transformer windings are indicated by "s" and "f". The start of the low impedance winding of a PT-156 or P-T157 transformer is the blue lead. The finish is the red lead. The green lead next to the red lead is the start of the center tapped high impedance winding. The green lead next to the blue lead is the finish. If Stancor A53-C transformers are (is) being used, the color coding is different. The start of the low impedance winding is the red lead, the finish is the blue lead. The green lead of the center tapped winding next to the blue lead is the start, and the green lead next to the red lead is the finish.

The insertion loss values shown below are were measured using A.E.S. P-T157 transformers. Stancor A53-C or generic "3:1 AIT" units will perform somewhat worse, as mentioned above. If you are going to use a generic "3:1 AIT", keep in mind that all or most of the extra insertion loss at 0.3 kHz can be eliminated by using the correct capacitor in series between the transformer and headphones.

A very low loss transformer that can be used to transform a 1 Megohm source down to closely impedance match a 12k AC ohm load is the small UTC O-15 'Ouncer' transformer. Its insertion power loss is less than 1 dB from 0.3-3.3 kHz.

Here are general specifications for the A.E.S. P-T157, Stancor A-53C and generic "3:1 AIT" Inter-stage transformers: Single Plate (10,000 Ohms) to push-pull grids (90,000 Ohms). Overall turns ratio: 1 to 3 Primary to Secondary. Max. Primary DC: 10 mA. These transformers are still relatively cheap and usually available at Hamfests, personal junk boxes and Used Component Vendors.

Part 3 - Transformer configurations for use mainly with Sound Powered Headphones

Now we will talk about some other transformer configurations that are suited for use with Sound Powered phones: UTC LS-10, UTC A-10, UTC A-12, Amertran 923A and UTC C-2080, as well as many others. The UTC A-10 and A-12 have the same terminal impedance specifications as the LS-10 and will probably perform similarly. Some of these transformers are currently quite expensive. For some lower cost options, see Part 5 of this article for some generic transformer specs., or consider the last two connections shown in the chart above. Shown below are loss measurements using a physically very small, but very low cost transformer, the MOUSER TM-117 as well as two excellent small low loss transformers from the CALRAD line.

At the end of this Section (#3), measurements on a combination of two transformers are be shown that enable 900k to 1200 ohm and 470k to 1200 ohm impedance transformation.

Six measurements on the TM-117 are shown. The first test of the transformer is with the input and output resistance values specified by the Manufacturer, but at a low output signal level. The second is for a TM-117 driven and loaded by the resistances of 24k ohms primary and 300 ohms secondary instead of 50k ohms primary and 1k ohms secondary. The 24k ohm level is close to that delivered by a generic 1N34A diode when detecting a weak signal. The next three measurements are for four TM-117 transformers interconnected to give a transformation ratio four times greater than one gets from one transformer alone. The primaries are connected in series and the secondaries are connected in series/parallel. The resultant primary and secondary are connected as an autotransformer. Results are given from measurements made at three output power levels. The last measurement is with the transformers connected for a 1,200 Ohm output instead for a 300 Ohm output. Most Sound Powered elements I have seen have an AC impedance of about 600 Ohms when averaged over the frequency range of 0.3-3.3 kHz. When used as a 1,200 Ohm transformer load, the two elements should be connected in series. When used as a 300 Ohm load, the elements should be connected in parallel. Remember that the insertion loss near 0.3 kHz can usually be reduced by placing a proper capacitor in series with the connection from the transformer to the sound powered headphones.

The transformer loss figures for the UTC and AMERTRAN transformers were measured at an output power of about -60 dBm. Performance is retained at output power levels much less than -60 dBm. A voice signal at this power level will be quite soft, but understandable through most sound powered headphones.

The MOUSER transformer deserves special discussion since it is so low in cost (available at Mouser Electronics (http://www.mouser.com ). Frequency response and distortion: The loss figures at two different power levels for a TM117 purchased in March of '00 are as follows: Output power level of +15 dBm: 2.8 dB @ 0.3 kHz, 1.9 dB @ 1.0 kHz and 6.4 dB @ 3.3 kHz. Output power level of -60 dBm: 11.1 dB @ 0.3 kHz, 1.8 dB @ 1.0 kHz, 5.7 dB @ 3.3 kHz and 5.4 dB @ 0.6 kHz. The 0.3 kHz loss is greater at a power level of -60 dBm than at +15 dBm. Why? The core laminations of the TM-117 (and many other very small transformers) have low permeability at the low magnetic flux levels generated by the -60 dBm signal. This low permeability is called initial permeability. The initial permeability, in combination with other factors, results in the transformer having a specific shunt inductance (at low signal levels). This shunt inductance controls the low frequency roll-off of the transformer. At higher flux levels (signal levels), but before saturation occurs, the permeability increases to an "effective permeability" value which can be several times greater than the initial permeability. This means that the transformer shunt inductance is higher at the higher signal level and the low frequency roll-off is much reduced. There may be some production unit-to-unit variation in the low frequency response of the TM117. One that I bought about a year ago showed 2.5 dB less loss at 0.3 kHz than the one tested above. Some low frequency harmonic distortion is generated in the changeover region from initial to effective permeability. This can easily be seen on a 'scope, especially at 300 Hz sine wave. I doubt that it would be very noticeable in actual crystal radio set use.

One can see from lines three, four and five of data in the TM-117 Insertion Loss Chart above, that the loss at 0.3 kHz, relative to that at 1.0 kHz, gets less as the output power level is increased. The loss at 1.0 kHz is minimum at the -42 dBm output power level. The greater 1.0 kHz loss at the -72 dBm power level is caused by the reduced shunt inductance as explained above. The increase in 1.0 kHz loss at -42 dBm occurs because the core is getting closer to saturation. The loss at 3.3 kHz in the four-transformer configuration is greater than that for one transformer shown on line 2 because the primary-to-secondary capacitance of transformers A and B is effectively connected from high impedance points and ground, thus rolling off the high end response. The single transformer in line 2 is wired so that the primary-to-secondary capacitance is not in shunt across the primary to ground.

The CALRAD line of small transformers offers two types that are suitable for use in transforming a high diode detector output resistance down to 300 or 1200 Ohms to drive SP phones. Their insertion loss is quite low and within a fraction of a dB of that of the UTC LS-10. One distributor of CALRAD transformers is Ocean State Electronics, 6 Industrial Drive, P.O. Box 1458, Westerly, RI. http://www.oselectronics.com/ (they call these transformers (Mini Audio Transformers). The two transformers are #45-700, spec'd to transform 100k to 1000 Ohms and #45-703, spec'd to transform 200k to 1000 Ohms. They sell for about $5.95 ea. The following chart shows the measured performance of a single transformer and of combinations of two. Lines #1 and 2: Primaries are in series, secondaries in parallel. Line #3: Primaries are in parallel, secondaries in series. Performance is very good, especially so, considering the price.

Note: The hot lead of the high impedance winding should always be the red lead. The hot lead of the low impedance winding should be the white lead. The high impedance windings are connected in series in lines 1, 2, 6 and 7. They are in parallel in line 3.

The low impedance windings are connected in parallel in lines 1, 2, 6 and 7 with leads of like color connected together. The hot low impedance output connection is to the white leads. The other two joined leads go to ground. The low impedance windings are connected in series in line 3.

One must properly phase the windings when two transformers are used. The lead from the hot end of the high impedance winding of transformer #1 should be connected to the diode. Its cold lead should go to the hot lead on transformer #2. The cold lead of transformer #2 should go to a parallel RC, the other end of which should either go to ground in lines 1, 2, 3, and 7 or to the hot low impedance output in line 6 (autotransformer connection). In line 7, transformer #1 should be the 45-703.

A UTC O-15 'Ouncer' transformer can be combined with a Bogen T-725** to make an excellent low loss transformer assembly for matching a wide range of headphone impedances, as well as an 8 ohm speaker, to a 1.35 Meg source resistance. See Fig. 4a. Insertion Power Loss is 2.6 dB @ 0.3 kHz*, 1.2 dB at 1 kHz and 1.7 dB @ 3.3 kHz. Note, that for these measurements, the housing of the O-15 was left ungrounded to eliminate the approximately 20 pF stray capacity from terminal #4 to the case. This reduces loss at 3.3 kHz, but might introduce hum in some applications. An alternative connection that matches to a 1 Meg source is shown in Fig.4b. This lowers the transformation ratio to reduce the effect of external stray capacitance-to-ground from crystal set components connected to the high impedance point. It also reduces sensitivity to hum pickup if the case of the O-15 is left ungrounded. The result is a small 0.5 dB loss reduction loss at 3.3 kHz when that stray capacitance is 16 pF. The Bogen T-725 transformer is available from Dave Schmarder's "Hobby Electronic Parts" at: http://www.1n34a.com/catalog/parts.htm . The UTC Ouncer O-15 transformer is hard to find, but sometimes shows up on e-Bay.
*See the asterisk at the end of the Mouser insertion loss table above.

The R1 C1 combination is sometimes called a "benny". It is used to reduce audio distortion sometimes encountered on strong stations. A good value for the pot, R1, is 1-3 Megs, preferable with an audio taper. C1 is not critical. A value of 0.1 uF is suggested.

A typical diode for use with this transformer assembly is a one having a saturation current of about 22 nA, such as the Agilent 5082-2835 or HSMS-2820. The weak signal audio output resistance of such a diode, as well as the input audio resistance of this transformer assembly shown in Fig. 4a are each about 1.35 Megs, making their parallel combination about 675k ohms. If the total shunt capacitance at this point is about 70 pF, audio frequencies above 3.3kHz will be attenuated by more than 3 dB. This capacitance consists of the sum of the windings capacitance of the transformer assembly referred to its input, wiring capacity to the diode and the junction capacity of the diode, etc, all in parallel with the RF bypass capacitor of the detector (C9 in Fig. 5 in Article #26). When using this transformer assembly, if the audio high frequencies seem deficient, try reducing that capacitor (C9), or maybe eliminating it and depending upon the other capacitive elements for RF bypassing. If one possesses good high frequency hearing, a higher impedance tap than normal may strengthen the highs. This is because the impedance of magnetic headphones is not constant. It rises as frequency increases, therefore, a better impedance match will exist for high frequencies when a higher impedance tap than normal is used. See "The effect of source impedance on tone quality" in Article #2.

**Note re the Impedance Table for the Bogen T725 transformer, above: The Bogen Speaker Matching transformer is designed to be used when one wishes to drive multiple 8-ohm speakers, distributed over a wide area, from a single audio source, e.g., a public-address system. In order to limit I-R losses in the distribution line, the system is operated at a higher than normal impedance and voltage. For example, a 100-watt amplifier, with a 49-ohm output impedance, will deliver 70 volts to the line. At each speaker, a transformer is used to connect the 70-volt line to the speaker voice-coil. The line-to-voice-coil transformer has multiple primary taps to allow the power delivered to each speaker to be individually adjusted to suit system requirements. The taps on such transformers are often labeled with the power they will draw from a 70-volt, or sometimes a 25 volt line. When adding an 8 ohm speaker to a system with a Bogen T725, it is first connected to the pink wires of the T725. One then selects a tap to connect to the audio source, depending upon how loud one wants the speaker to be (taps white through brown), with black as common. The step-down turns ratio between [(white through red)-to-black] and [pink-to-pink] sets the volume. Basically, to accomplish its objective, the T725 was designed to transform an 8 ohm speaker load to one of various other impedances between 150 to 40k ohms as shown in the Table in Fig 4, above.

Now let us get out of the context of sound distribution and into crystal set audio impedance matching. Consider the tapped black through white winding of the Bogen T-725 as just a conventional autotransformer designed for maximum efficiency (low loss) when used at the impedances shown. There is no "magic" in the "nominal" values of 150 through 40k ohms assigned to the various colored taps. The autotransformer can just as well be used at impedances a multiple higher or lower than those shown, although with some extra insertion power loss. It seems that the convention of assigning impedance values to the taps has fostered some confusion. For instance, one should not think that the "right" impedance to connect to the green wire is 2.5k ohms. In the BT- Ultimatch (see Part 4, below), the settings of the input and output switches connected to T725 should be set for minimum insertion power loss. Probably the 'nominal" impedance of the output tap used will be close to that of the load but not necessarily the same.

Part 4 - The BT-UltiMatch, a modified version of Steve Bringhurst's UltiMatch. Insertion power loss and input resistance measurements when using a selection of various 'Stanley-type' transformers or an UTC O-15 for T1 for the input transformer are displayed

Steve Bringhurst's UltiMatch (see http://www.crystalradio.net/soundpowered/matching/index.shtml#UltiMatch) on Darryl Boyd's Site provides a convenient low-loss way to provide audio impedance matching between the output resistance of a diode detector and the average impedance of headphones or a speaker. The BT-UltiMatch is somewhat different from Steve's, the differences being the replacement of Steve's SW5 with a single-pole 10 point rotary switch and provision for switching in an UTC O-15 in place of the "Stanley-type" transformer used for T1. The two10-point rotary switches enable one to connect any of the taps of T2 to the secondary terminals of either T1 or T3, as well as to the output capacitors C2-C6. This provides for a greater range of impedance transformation and a further reduction in power loss (especially at high source resistances) than when one is limited to using only the brown or red wires of T2. Provision is also made for switching in a UTC O-15 Ouncer transformer in place of the Stanley-type unit.

Two sets of measurements were made using 300 and 1200 ohm resistive loads (typical average impedance of SP headphones having both elements connected in parallel is 300 ohms, in series, 1200). The input voltage at 1 kHz was series-connected through a selection of source resistors to the input of the BT-UltiMatch. The level of this voltage was adjusted to produce about 10 mV RMS across the output load of 1200 ohms (5 mV when measuring with a 300 ohm load). See Part 5 of this Article for info on how the BT-UltiMatch loss measurements were made.

Parts list

T1 - "Stanley-type" 100k-100 ohm transformer, available from Fair Radio Sales as # T3/AM-20
T3 - UTC Ouncer O-15 1 meg-10k ohm transformer
R1 - 2 or 3 Meg log taper pot or, a 1 Meg log taper pot with provision for switching in a series resistor to increase the total resistance to 2 Megs if low saturation current diodes (having a high axis-crossing resistance) are to be used
C1 - 0.22 uF capacitor
C2 - 4.7 uF non-polar capacitor
C3 - 2.2 uF non-polar capacitor
C4- -1.0 uF non-polar capacitor
C5 - 0.47 uF non polar capacitor
C6 - 0.22 uF non polar capacitor
SW1, SW2 - Single pole 12 position (only 10 used) rotary switches. Designate SW1 and SW2 switch positions with the nominal impedance values given in the Table in Fig 5
SW3 - One pole, 6 position rotary switch
SW4 - Two pole, 4 position rotary switch

Operation of the BT-UltiMatch

Four modes of operation are provided by SW4:

This most common mode uses a "Stanley type" transformer as the input transformer, T1. For use with a wide range of diodes having moderate axis-crossing resistances, such as the ITT FO-215 germanium diode (Is~100 nA).
Uses UTC O-15 Ouncer transformer for T1. Use with diodes having high axis-crossing resistances such as the Agilent 5082-5235 Schottky diode (measured Is~15 nA, not the spec sheet value of 22 nA), or 2-3 in parallel.
Does not use input transformer T1. Use with diodes having low axis-crossing resistances such as the 1N34A germanium diode (Is~600 nA).
Does not use input transformer T1. Use for general purpose impedance transformation, working with T2 only (SW1 and the "benny" - R1,C1 are out of the circuit).

J1 should be connected with a very short cable (when using very low Is diodes) to the diode output of a crystal set, the usual audio source. J2 is connected to headphones or a low impedance speaker. The "nominal" impedance designations on SW1 and SW2 are for reference and do not always represent the settings for the least insertion power loss. When starting out to match real world headphones or a speaker to the diode output of a crystal set, do the following:

Select a setting for SW4, depending upon the estimated Is of the diode being used (see Tables 1 and 2 in Article #27 for some help on this).
Set the "nominal impedance" of SW2 to the expected average impedance of the output load (see Article #2 for info on how to obtain this info).
Set SW3 to the "thru" position.
Adjust SW1 for loudest volume.
Adjust R1 for minimum distortion.
The optimum settings for SW1 and SW2 are interactive. Try higher and lower settings for SW1 , then tweak SW2 to see if greater volume is available, then iterate.
Try different settings for SW3 to see if bass response improves.

Table 8 - Insertion power loss in a BT-UltiMatch @ 1 kHz using a selected Stanley transformer TF-1A-10-YY "D" or an UTC Ouncer O-15 transformer for T1. Measurements are made with different series-connected source resistances and with load resistances of 300 or 1.2k ohms. SW1 and SW2 were adjusted for maximum output
Transformer	Source and load resistances in ohms, insertion power loss in dB
Stanley "D"	2.2 Meg, 300; -2.59	1.0 Meg, 300; -1.41	470k, 300; -0.70	220k, 300; -0.69	100k#, 300; -0.94
UTC O-15	2.2 Meg, 300; -1.61	-	-	-	-
Stanley "D"	2.2 Meg, 1.2k; -2.50	1.0 Meg, 1.2k, -1.37	470k, 1.2k; -0.94	220k, 1.2k; -0.95	100k#, 1.2k; -0.84
UTC O-15	2.2 Meg, 1.2k; 1.54	-	-	-	-

Table 8A - Nominal** settings for SW1 and SW2 taps in ohms for minimum insertion power loss, using a UTC or selected Stanley transformer for T1
Transformer	Source resistance, load resistance of 300 and [T1 and T2 nominal tap settings] in ohms
Stanley "D"	2.2 Meg; 600, 300	1.0 Meg; 300, 300	470k; 1.2k, 1.2k	220k; 600, 1.2k	100k#; 40k, 150
UTC O-15	2.2 Meg;, 10k, 150	-	-	-	-
Transformer	Source resistance, load resistance of 1.2k and [T1 and T2 nominal tap settings] in ohms
Stanley "D"	2.2 Meg; 1.2k, 1.2k	1.0 Meg; 600,1.2k	470k; 300, 1.2k	220k; 300, 2.4k,	100k#; 40k, 600
UTC O-15	2.2 Meg; 10k, 600	-	-	-	-

** See Table of Impedance taps in Fig 5 showing nominal impedances for the various taps on the Bogen T-725 transformer

# SW4 set to position 3

Table 9 - Insertion power loss (dB) in a BT-UltiMatch @ 1 kHz using various transformers for the input transformer with various series-connected source resistances. Load resistance of 1.2k ohms. SW1 and SW2 were adjusted for maximum output
Transformers	Series-connected source resistance in ohms; insertion power loss in dB
Stanley "C"	-	1.5 Meg: -1.95	1.0 Meg: -1.51	470k: -0.98	220k: -0.97	-
Stanley "Z"	-	1.5 Meg: -2.26	1.0 Meg: -1.75	470k: -1.03	220k: -1.00	-
Stanley "D"	2.2 Meg: -2.50	1.5 Meg: -1.81	1.0 Meg: -1.37	470k: -0.94	220k: -0.95	100k#, -0.84
UTC C-2080 "A"*	-	1.5 Meg: -1.73	1.0 Meg: -1.36	470k: -0.99	220k: -0.96	-
UTC C-2080 "B"	-	1.5 Meg: -1.90	1.0 Meg: -1.46	470k: -0.93	220k: -0.96	-
No name TA-18.071*	-	1.5 Meg: -1.81	1.0 Meg: -1.42	470k: -0.92	220k: -0.97	-
UTC O-15 Ouncer Tx	2.2 Meg: -1.54	-	-	-	-	-

* The polarity of one winding in each of these transformers was reversed during its manufacture. Measurements were made with terminals 1 and 2 interchanged to correct the condition. The polarity assumption used in the BT-UltiMatch for a Stanley-type T1 is as follows: If an AC voltage is applied from terminals 3 to 4, a voltage of the same polarity will appear from terminals 1 to 2. It is recommended that anyone building a BT-UltiMatch check the polarity of the internal terminal connections of the T1 transformer with a 'scope.

Table 10 - Input resistance of a BT-UltiMatch driven from various series-connected source resistances, terminated by a 1200 ohm load and adjusted for minimum loss
Transformer used for T1	Series-connected source resistance	BT-UltiMatch input resistance
Stanley TF-1A-!0-YY "D"	100k	171k#
Stanley TF-1A-!0-YY "D"	220k	286k
Stanley TF-1A-!0-YY "D"	470k	517k
Stanley TF-1A-!0-YY "D"	1 Meg	751k
Stanley TF-1A-!0-YY "D"	2.2 Meg	1.10 Meg
UTC O-15 Ouncer	2.2 Meg	1.68 Meg

# SW4 set to position 3

Notice, since the transformers are mostly not used at their design-center impedances, settings for minimum insertion power loss do not always coincide with an impedance matched condition.

Part 5 - How to Measure the approximate Insertion Power Loss of any Audio Transformer
or Compare its Performance to that of an Ideal no-loss Transformer

The equipment needed are an audio sine wave generator, an assortment of resistors (preferably not a resistance box), and a high sensitivity scope or DVM. The use of a vertically calibrated scope is preferable to a DVM, as one can see that the waveform is clean and without appreciable hum or noise. A difficulty with this approach is that one must make sure that the scope decade attenuator as well as the 10X switch on the probe are accurate. I use the scope probe switched to 1X when reading the low voltage secondary voltage and to 10X setting when measuring at the higher voltage primary. The high input impedance of the probe prevents excessive loading of the high impedance primary, thus reducing the voltage there and causing an incorrect reading. When a DVM and a 'scope of adequate sensitivity are available, the best approach, and the one I now use, is to connect them in parallel. This provides the relatively high precision of a reading with the DVM along with the ability to monitor the voltages for purity (low distortion of the sine wave measuring wave form and low noise).

Connect the hot lead of the generator to the high impedance primary of the transformer through a resistor of value equal to Rs. Rs should be equal to the expected output resistance of the diode detector. Connect a load resistor of value Zh (expected effective impedance of the headphones) to the secondary. Connect all grounds to a common point.

Tune the generator to the first frequency of measurement, say 1000 Hz. Connect the scope or DVM to the low impedance secondary. Adjust the audio generator to as low a level as possible while still being able to get an accurate reading of the voltage without error from hum and noise. Read this voltage and call it E3. Now connect the scope probe to the hot end of the primary. Read that voltage and call it E2. Connect the scope probe or meter to the actual generator output (not the transformer hot lead). Read this voltage and call it E1. Calculate insertion loss: Loss=10*log{4*RS*[(E3/E1)^2]/Rl} dB. Also take measurements at 300 and 3300 Hz. If the 300 Hz loss is much greater than the 1000 Hz loss, a transformer with a higher primary inductance is needed. If the 3300 Hz loss is much higher than the 1000 Hz loss, the transformer has too high a winding capacitance for the primary source resistance (RS) selected. If the loss at 1000 Hz is above about 2 dB, a better transformer probably exists. Hopefully all readings will be better than -2 dB.

If the transformer is doing a good job of impedance matching RS to Rl, E2 will be about 1/2 the value of E1 and the transformer insertion loss will be at about its minimum. If E2 is much lower than 1/2 of E1, a greater impedance transformation (turns ratio squared) is needed. If the transformer has taps on the secondary, using a lower impedance tap might improve results. If E2 is higher than 1/2 of E1, the impedance transformation ratio is too large and a higher impedance secondary tap should be tried (if available). It is assumed here that reactive mismatch from transformer shunt inductance and distributed capacitance is negligible. It's usually best to make the 1/2 voltage measurement at the frequency of minimum loss (usually about 1 kHz for audio transformers.

In this series of Articles the statement is often made or implied that power loss in an audio transformer is at a minimum when the input is impedance matched. This is not strictly true. If a transformer has internal resistive power loss and is matched at its input, the output will, in general, be mismatched. A simultaneous matched condition at both input and output is usually impossible unless the transformer has no internal losses, or its series and shunt losses are in the correct proportion. A real world transformer delivers its minimum loss when the input and output mismatches (S parameter return losses) are equal. Verification of this condition is both difficult and unnecessary because the two loss values (matched input vs equal mismatch at input and output) normally differ very little. This being the case, one can say, for practical purposes, that the minimum insertion power loss occurs when the input is impedance matched.

An easy way to compare the performance (loss) of a particular transformer with that of an ideal no-loss transformer of just the right transformation ratio is to build and use the 'Unilateral Ideal Transformer Simulator' described in Article #14.

Tip: If hum and noise are a problem, place the scope (or DVM), signal generator transformer and all leads on a metal ground plane connected to the scope ground. Ordinary kitchen aluminum foil is suitable for the ground plane.

Note: If one has some sort of audio impedance measuring device and desires to measure the shunt inductance of an audio transformer, make sure the measurement frequency is low enough so that the transformer winding capacitance does not interfere with accuracy. A transformer, tested above, that is very good for many crystal radio sets when driving 300 ohm headphones is sold by Fair Radio Sales Co. http://www.fairradio.com/ as #T3/AM20 (similar to UTC #2080). Its winding capacitance is at approximate resonance with its shunt inductance at 1 kHz. This is good design practice since it minimizes insertion power loss at the (approximate) geometric center of the audio band. A measurement of its unloaded (high impedance winding) Z at 1 kHz yields a result of "infinite" shunt inductance in parallel with a resistance of more than a Megohm. A measurement at 300 Hz gives a result of several hundred Henrys. A measurement at 3300 Hz would show a capacitive, not inductive impedance.

Part 6 - Some practical suggestions on where to get and how to identify transformers
that may perform well with sound powered headphones

Here are some generic transformer specifications, which when met, probably indicate that the transformer will exhibit low insertion loss when used to drive sound powered phones in a crystal radio set. A transformer obtained at a Hamfest, junk box or Surplus Dealer that meets these specs. will probably cost substantially less that the UTC and Amertran transformers. Fair Radio Sales Co. at http://www.fairradio.com/often has suitable transformers available at reasonable prices.

Wide frequency response specification such as +/- 1 dB, 20-20,000 Hz: A transformer having a Manufacturer's specified operating frequency range from, say, 200-5,000 Hz will probably have several dB more loss than a wide band unit when both are sourced and loaded with resistances that reduce their bandwidth to covering only the 0.3-3.3 kHz range. The reason for this is that we usually want to operate the transformer with primary source and secondary load resistances several times higher than that which the manufacturer specifies. This always narrows the transformer pass-band. We should shoot for a final pass-band of 0.3 - 3.3 kHz, or so.
High impedance winding specification: Single grid, preferably push pull grids, single plate or preferably push pull plates. The impedance level, if specified, will usually be between 20,000 and 80,000 Ohms. The high impedance winding is the one to connect to the diode detector output.
Low impedance winding specification: Low impedance mike, pickup, multiple-line or simply a number between 100 and 1000 (Ohms). Several taps may be supplied to enable various impedance levels. The specification might be: 50, 125/150, 200/250, and 333, 500/600 Ohms. This winding is the one to which the sound powered phones are to be connected.
The correct low impedance tap to use for connecting the sound powered phones may be calculated as follows:

Decide the audio load resistance to be presented to the detector. Let's select 200,000 Ohms. (See Articles #1 and #4 for info on how to determine this value). Assume that the sound powered elements are connected in series. This will typically result a headphone average impedance of 1,200 Ohms. Calculate the needed impedance transformation ratio as: 200,000/1,200 = 167. Note the Manufacturer's specification for the high impedance winding of the transformer. (If you don't know what it is, estimate 80,000 Ohms.), and divide it by 167. Select the Manufacturer's low impedance winding tap specification (if you have that info) that most closely equals the value calculated above. If you are using the 80,000 Ohm estimate, the desired tap impedance would be 80,000/167 = 479 Ohms. Call this number A. Now check what the result would be if the sound powered elements were connected in parallel. They will now present an effective impedance of 300 Ohms and require an impedance transformation ratio of 200,000/300=667. The desired Manufacturer's tap marking will now be 80,000/667 = 120 Ohms. Call this number B. Pick the number A or B, whichever is closest to an available transformer tap marking. Connect the phone elements appropriately. Note that we are using the transformer at a higher impedance level than that for which it was designed. What we lose is by doing this is audio bandwidth and a small increase of insertion loss. We don't need the 20-20,000 Hz range anyway, do we? What we gain is an ability to transform headphone impedance to a higher value than if we used the manufacturer's ratings.

If you have a transformer on which you have no specs. except that it is designed to couple from a low impedance to push-pull grids, a grid, push-pull plates of a plate or just "high impedance", connect that winding to the crystal diode and experiment with connecting the headphones to the various taps provided on the low impedance winding. Do this experimentation using a weak signal and pick the connection that gives the greatest volume.

#5 Published: 10/22/99; Last revision: 03/30/2008
060410

Low-loss impedance matching for magnetic and piezoelectric headphones, measurements on many audio transformers, and a transformer loss measurement method