The best diode and audio transformer for a crystal set, and a way to measure diode saturation current
by Ben H. Tongue
Here is a practical way to determine the diode and audio output transformer impedance matching characteristics needed to maximize sensitivity and selectivity for weak signals and to reduce strong-signal audio distortion in a Crystal Radio Set. Unfortunately, this may be an iterative process.
What we have done here is to minimize loading on the tuned circuit from the diode detector. If this diode loading is made negligible, using a resistor of value equal to that of the resonant resistance of the tuned circuit will reduce the RF voltage to 0.5 of what it was before the resistor was placed. Here, the diode has been given a high resistance DC load to further reduce its loading effect on the tuned circuit (the 10 Meg resistor connected in place of the headset). The detector is used as an indicator of the RF voltage across the tank circuit. The diode will be operating somewhere between linear and square law. That is where the 0.35 comes from (geometric mean of 0.5 and 0.25). A Better approach, if one has a high sensitivity scope good to above 1.0 MHz, is to disconnect the diode from the tuned circuit. Then very lightly capacitively couple the scope to the tuned circuit and use it as a measuring tool when placing the resistor across the tuned circuit. Then of course, one would use the 0.5 figure for voltage reduction since the measurement is linear. Bear with the problem of the measured voltages jiggling up and down due to modulation. Just estimate an average. (See Article #0 for information on diode Saturation Current and Ideality Factor.)
2. A good diode to use in the crystal radio set above, for weak signal reception, is one with an axis-crossing resistance equal to Rr. A diode that has an axis-crossing resistance of Rr is one having a Saturation Current of Is = (25,700,000*n)/Rr nanoAmps. The ideality factor of the diode (n) is an important parameter in determining very weak signal sensitivity. If all other diode parameters are kept the same, the weak signal input and output resistances of a diode detector are directly proportional to the value of n. Assume a diode with a value of n equal to oldn is replaced with an identical diode, except that it has an n of newn; and the input and output impedances are re-matched. The result will be a detector insertion loss change of: 10*log(oldn/newn) dB. That is, a doubling of n will result in a 3 dB drop in power output, assuming the input power is kept the same and impedances are re-matched. This illustration shows the importance of a low value for n. Back leakage resistance should be low and the diode series resistance (Rs) should also be fairly low. Diode barrier capacitance should be fairly low (6 pF or less) . Schottky barrier diodes usually have low series resistance, barrier capacitance, Ideality Factor and very low back leakage. The challenge is to get a diode reasonably close to the correct Is. (If it's within 0.3 and 3 times the calculated value, you won't notice much difference.) A simple way to check for back-leakage is to measure the back resistance of the diode with a non-electronic VOM such as the Triplett 630 or Weston 980. Use the 1000X resistance switch position. If no deflection of the meter can be seen, the diode back leakage is probably OK. Another way is to place a DC blocking capacitor in series with the diode. If the audio becomes very distorted, the diode leakage is low (this is the desired result). A value of 1000 pF or so is OK for this test.
Here is an easy way to determine the approximate Is of a diode. Forward bias the diode at about 1.0 uA. A series combination of a 1.5 volt battery and a 1.5 Meg resistor, connected across the diode will do this. Measure the voltage developed across the diode with a DVM having a 10 Meg input resistance. Calculate Is=667*(Vb-Vd)/(e^(Vd/(0.0257*n))-1) nA. e = base of the natural logarithms = approx. 2.718, ^ = "raise the preceding number to the power of the following number", Vb = voltage of the battery, Vd = voltage across diode and n = diode Ideality Factor (Emission Coefficient). I suggest using an estimate of 1.12 for n. Most good detector diodes seem to have a n between 1.05 and 1.2 A method for measuring both n and Is is shown in Article #16. Measurements on 1N34A germanium diodes at various currents show that the values for Is and n are not really constant, but vary as a function of diode current. Is can increase up to five times its value at low currents when currents as high as 400 times Is are applied. However, germanium diodes I have tested exhibit a fairly constant n and Is when measured at currents below about six times their Is. A rectified current of about 6 times Is corresponds to a fairly weak signal. The following chart shows some results from measuring several diodes at a current of 1.0 uA. The calculated low-signal-level value of the diode junction resistance Rj= 0.0257*n/Is is is also given. Note the wide variation among the various diodes sold as 1N34A. Schottky diodes, as a rule are fairly consistent from unit-to-unit. The Agilent '2835 measured 11 nA, and many others test close to this value. I think that many years ago early production '2835 diodes probably matched the Spec. sheet value of 22 nA for Is. Over the years, I would guess that the average value was allowed to drift in order to optimize other more important parameters (for most applications) such as reverse breakdown voltage. BTW, Is is not a guaranteed 100% tested production spec.
Caution: If one uses a DVM to measure the forward voltage of a diode operating at a low current, a problem may occur. If the internal resistance of the DC source supplying the current is too high, a version of the sampling voltage waveform used in the DVM may appear at its terminals and be rectified by the diode, thus causing a false reading. One can easily check for this condition by reducing the DC source voltage to zero, leaving only the diode in parallel with the internal resistance of the source connected to the terminals of the DVM. If the DVM reads more than a tenth or so of a millivolt, the problem may be said to exist. It can usually be corrected by bypassing the diode with a ceramic capacitor of between 1 and 5 nF. Connect the capacitor across the diode with very short leads, or this fix may not work.
If one wishes to screen a group of diodes to find one having a specific Is, use the setup described above. Substitute the desired value of Is into the following equation: Vd=0.0282*ln(667*(Vb-Vd)/Is+1) volts. 'ln' means natural base logarithm and Is is in nA. A diode having a Vd equal to the calculated value will have approximately the desired Is.
Here are some tips to consider when measuring diodes: Keep all leads short and away from 60 Hz power wires to minimize AC and electrostatic DC pickup. Place a grounded aluminum sheet on the workbench, and under the DVM and other components to further reduce spurious pickup by the wiring. A piece of grounded kitchen aluminum foil will do nicely for the aluminum sheet. You may find that the reading of Vd slowly drifts upwards. Wait it out. What you are observing is the temperature sensitivity of Vd to heat picked up from handling the diode with your fingers. Let the diode return to room temperature before taking data.
Many glass diodes exhibit a photoelectric effect that can cause measurement error. Guard against it by checking to see if a diode current reading changes when the light falling on the diode is changed.
Note that these values for Is and n are not cast in stone. Is can easily vary by 2:1 or more from diode to diode of the same type.
Multiple similar diodes may be paralleled to increase Is. Is is increased proportionally to the number of diodes in parallel. Four identical diodes in parallel will give a saturation current four times the Is of one alone. For purposes of Crystal Set design, diodes should not be placed in series. SPICE simulation shows that if two identical diodes are connected in series, the combination will perform the same as one of the diodes alone, but having a doubled value for n. This increased value of n will reduce weak signal sensitivity.
In a particular crystal radio set Is can vary quite a bit without a great effect on performance. One can be in error by several times and still get good results. Too high an Is reduces selectivity on weak signals. Too low a value reduces sensitivity to weak signals and causes excessive audio distortion.
Many times the question is asked, "What is the best diode to use?" The answer depends on the specific RF source resistance and audio load impedance of the Crystal Set in question. At low signal levels the RF input resistance and audio output resistance of a detector diode are equal to 25,700,000*n/Is Ohms (current in nA). For minimum detector power loss at very low signal levels with a particular diode, all one has to do is impedance match the RF source resistance to the diode and impedance match the diodes' audio output resistance to the headphones by using an appropriate audio transformer. The lower the Is of the diode, the higher will be the weak signal sensitivity (volume) from the Crystal Set, provided it is properly impedance matched to it's circuit (see article #1). This does not affect strong signal volume. There is one caveat to this, however. It is assumed that the RF tuned circuits and audio transformer losses don't change. This can be hard to accomplish. It is assumed that the Rs, diode junction capacitance, n and reverse leakage are reasonable. If the diode you want to use has a higher Is than the optimum value, tap it down on the tuned circuit. If the diode you want to use has a lower Is than the optimum value, change the tank circuit to one with a higher L and lower C so that the antenna impedance can be transformed to a higher value and repeat step #1.
If you don't have a diode of the proper calculated Is, you can simulate what the result would be if you did have one by doing the following: Put a small voltage in series with the DC load resistor ground return (see point #4 below). If your diode has too low an Is, biasing the diode in the forward direction will improve sensitivity. If your diode has too high an Is, biasing the diode in the reverse direction will improve sensitivity. See Article #9 on the home page on how to build and use a "Diode Detector Bias Box".
4. The average audio impedance of the headphones should be transformed up to the value Rr by an appropriate audio transformer. The step-down impedance transformation ratio needed in the transformer is Rr/Zh. When connecting the transformer high impedance winding to the diode, put a parallel RC (a benny) in series with the ground connection . This will insure that the DC load on the diode can be made the same as the audio AC load. A good value for the R should be about equal to Rr. It's best to use a pot so that the value can be optimized at different signal levels. For minimum audio distortion at medium and high signal levels, the DC load on the diode should be the same as the AC audio load. The value of the C should be large enough to fully bypass the R for audio. A good value is C=5/(pi*2*300*Rr). The parallel RC will have less effect on reducing distortion or affecting selectivity when receiving loud signals if the transformed headphone load on the diode is lower than the diode output resistance, than if it is higher. For info on the impedance transformation ratios of various transformers see Article #5. The audio transformer should have a low insertion loss. Try to obtain one with less than 2 dB loss from 300-3300 Hz when measured at low Crystal Set signal levels. See Article #5 for info on how to measure transformer Insertion Loss.
5. Connect up the new diode and transformer and the parallel RC. Trim up the value of the R in the parallel RC for the least audio distortion on a loud signal. There should be an improvement in low signal volume and high signal audio distortion as well as better selectivity.
#4 Published: 10/02/99; Last revision: 08/22/2002