Here is a practical way to determine the diode and audio output transformer characteristics needed to maximize sensitivity and selectivity for weak signals and to reduce strong-signal audio distortion in a Crystal Set.  Unfortunately, this may be an iterative process.

1. Determine the RF output resistance at resonance of the tuned circuit driving the crystal while the Crystal Set is connected to its antenna.
2. Calculate the Saturation current (Is) that the diode should have. The ideality factor of the diode should be as low as possible.  Get an appropriate diode.
3. Know the effective impedance of the headphones to be used.
4. Calculate the impedance transformation ratio needed to transform the diode audio output impedance to that of the headphones.
5. Connect it all up.

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.

#2.  A good diode to use in the crystal set above, for weak signal reception, is one with a Saturation Current Is = (25,700,000*n)/Rr nanoAmps.  See Article # 15 for updated information on this.  The ideality factor of the diode 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.  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 (up to 10 pF is Ok). 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 0.5 and 2 times the calculated value, you'll never notice the 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.  A value of 1000pF or so is OK for this test.

Here is an easy way to determine the approximate Is of a diode.  Forward bias a diode at about 1.0 uA.  A 1.5 volt battery with a series 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 1.07 for n.  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, I have found that 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.  Here are 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 1N34A diodes.  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.  BTW, Is is not a guaranteed spec.

Here are some tips to use when estimating Is with the procedure:  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 extreme temperature sensitivity of Vd to temperature changes (probably picked up from handling with your fingers).  Most diodes exibit a photoelectric effect that can cause measurement error.  Guard against it.

Here are some Germanium diode measurements made using a Mathcad program written by Ray Waugh of Hewlett-Packard.  The value of Rs is determined from voltage drop measurements taken at 4.8, 5.0 and 5.2 mA.  The values for n and Is are determined from the diode voltage drop at 0.1 and 1.0 mA.  The values of n and Is shown below should be thought of as taken at an average current of about 320 uA.  In germanium diodes Is varies with diode current and will be lower than the values shown at signal levels giving rectified currents below 320 uA. (Measurements at very low currents show that the Is may go as low as 1/5 the values shown.  For Schottky diodes, the value of n and Is seem to be independent of diode current.
 

Here are the catalog specifications for some Agilent (formerly Hewlett-Packard) Schottky Barrier diodes:
 

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 an n four times the Is of one alone.  For purposes of Xtal Set design, diodes should not be placed in series. Get a diode of the correct Saturation Current, Is, or create one by paralleling several similar diodes of the same type.  It's not very critical. One can be in error by several times and still get good results.  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 Xtal 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 (for maximum sensitivity), 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.   The lower the Is of the diode, the higher will be the low signal sensitivity (volume) from the Xtal Set, provided it is impedance matched to it's circuit (see article #1 and 15).  However, 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 may be hard to accomplish.  It is his 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".
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#3. Estimate the audio impedance of magnetic phones as 6 times the DC resistance.  Alternatively, build the "Headphone Effective Impedance" measuring device described in article #2 on the home page and use it to determine the headphone impedance. Call this impedance Zh.

#4. The average audio impedance of the headphones should be transformed up to the value Rr.  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 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 Xtal 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.

Published: 10/02/99;  Last revision: 04/25/01