The plot above shows the relationship between diode Is and Rd. Rd is calculated via the equation Rd = VT * n / Is where VT is the thermal voltage = k * T / q = 0.0257V at room temperature and Is and n are from the measured diodes. k is Boltzmann's constant = 1.38E-23 J/K and q is the electron charge = 1.609E-19 coulombs. On such a plot I can show lines of constant n, and plot the values for individual diodes for which I have spent considerable effort to determine the parameters Is, n and Rd (where Is is the diode saturation current, n is the ideality factor, and Rd is the diode resistance). On the plot it should be evident how changes in n or Is impact a diodes' Rd, specific changes that are dealt with in detail on the modeling plots below. Finally, I have included a fuzzy background region to indicate the region of "typical" tank Rf impedance. Matching the diode to the tank is a matter of finding a diode with both sensitive qualities and an Rd near equal to, but opposite in sign to the RF impedance of the tank. Those diodes with Is's in the 50 - 200 uA or so range have the possibility to match while connected to the top of the tank, that is, without the use of Q-lowering taps. Note that both resistance and impedance are frequency-specific so a match at one frequency will not remain across the broadcast band.
Information I have had most trouble to get my arms around is, just what are typical source RF impedences that we are attempting to match the diode to. Ben uses 700 kohm examples as a "fairly high" source impedence in one article and 280 kohm as a typical source impedence in another. From this I can imagine a range of "typical" source RF impedences to the diode as being in the low 100's and that is the region I have called attention to. One wishes their diode Rd to land in this region with respect to the RF tank they will be using. For low values of n, this suggests a Goldilocks region of about Is = 50 - 200 uA or so. Most germanium diodes I have measured have Is's in the 800 to 2000 uA range with correspondingly low Rd's, 15 - 50 kohms. As diodes are not variable, the only solution was to tap these diodes low on the coil to find a matching lower RF impedance. Note that the FO-215 and a couple other good Germaniums do manage to find their way to the goldilocks region, these are your prefered diodes. When I plot my HP2082-2835 schottky I am a bit surprised to see a high Rd over 2000. Still trying to see Ben's logic here! This is a work in progress...
Because the matching between the tank and diode is frequency-specific, ideally one would like an adjustable diode. Such is not the case except maybe in my dreams. The solution to deal with this I believe is to add a "Hobbydyne" or Selectivity Enhancement Circuit (SEC) between the tank and the diode. Such a circuit adds series capacitance (or both series and parallel capacitance in the case of a differential cap) which can help tune out the mismatch when the frequency changes off matched conditions. An excellent discussion of the SEC can be found on Dave Schmarders great web page.
A final note on the plot above. You will have noticed that I sub-divide germanium diodes into a "1N34A" class and a "1N270-277" class. This is a result of looking at their I / V characteristics on a plot of 1 - 2V DC versus 0 - 10mA scale. At such a scale the slope of the characteristic for the 1N270 class remains much steeper than that for 1N34 type diodes. As this is not seen as a distinguishing feature at the small-signal scales looked at here, I judge the chief difference between the two types lies in the diode series resistance Rs. This impacts strong-signals but is of no concern for small-signal DX work. Just so you know.
Here is an interesting plot taken from the text discussion in "Crystal Set Analysis" by Berthold Bosch. It presents received signal strength across the tuned circuit for various scenarios from threshold audibility to local blowtorch. This plot should be considered a single example specific to his location and antenna/ground system. In the text he describes his antenna an an inverted L 43m long (140') and 10m high (32'), an excellent antenna most of us do not have the real estate to erect, but offsetting this is a poor ground with Rg = 210ohms. Given the offsetting conditions I would imagine this is a good generic example of what received signal voltage and power levels presented across the LC circuit to the diode are likely to be. Bosch cited 40nV as the threshold of audible detectability (impedance matched conditions with 16kohm RF impedance / 4kohm DC phones) and for this plot I pushed it back to 20nV as it gave a superior regression fit.
This plot at left takes some actual diode I/V measurements rather than the models presented below and plots them along with the above RF voltage across the LC circuit versus RF power in mW. Here one sees that pushing for very very low Vf (via high Is / low n combinations) pushes the limit of detectable signal power from the antenna. At such minute power levels I imagine the reverse leakage current becomes significant and probably offsets the low operating point gains sought.
This section presents results of my attempts to calibrate my eyeball to the various principle diode parameters Is and n, and see what impact changes have on the characteristic curve, especially diode resistance Rd and approximate location of the Forward Voltage operating point Vf. My procedure was to start with my diode modelling spreadsheet and produce "ideal" characteristic curves (no effect of series resistance Rs) at low signal levels 0.0 to 0.5V / 0 - 100uA. As a "Base" case I modeled a PDG "Schottky'ish" diode with Is = 200 and n = 1. Modeled Rd for such a diode Rd = 129 kohm. All cases then will be compared to this base to see how changes in parameters Is and n impact the characteristic. Finally, I made two generic cases, one for a germanium and one for a silicon diode, and a specific case for the HP 5082-2835 diode.
My goal thus is to get an idea both visually and numerically as to what Is and n mean in terms of the diode resistance and characteristic, and how differences in them impact diode resistance Rd and operating point Vf, forward voltag drop. Rd here is calculated by the formula Rd = kT/q*n/Is, where kT/q = VT = 0.0256 at room temperature. [k is boltzmann's constant = 1.38E-23 J/K, T is the temperature in Kelvin, and q = electron charge = 1.609E-19 coulombs]. n is dimentionless and Is is in Amps. I have not included any information or model of diode reverse currents and one must keep in mind that for very low Vf the leakage goes up offsetting any advantage that pushing the operating point to very low voltages might offer. For diodes, the "operating point" or Vf is that point on the characteristic where the curvature is greatest and so rectification is most pronounced. This point is not defined and depends greatly on the scales used for your I/V plotting. For me, I have chosen to look at small signals in the 0 - 0.5V range with correspondingly low currents. I have "determined" the Vf by eyeball looking at my plots rather than defining any specific current level. This is a qualitative "feel" calibration.
The first case I look at is to simply view the effect of lowering the Is while leaving n unchanged. Note on this plot and all subsequent plots that the base is case plotted in blue. I plot the characteristic in both normal/normal and log/normal scales. With the first scale one "sees" the knee in the graph and can eyeball the operating Vf. The log normal scale shows the true characteristic and the slope of the log I vs V curve = n.
On this first plot one clearly sees that lowering Is, in this case from 200 down to 20, increases the diode resistance significantly, from 129 to 1290 kohms, and raises Vf from about 0.1V to about 0.15V or so. Note that as n was left unchanged the slope of the curve remains the same, it is merely pushed to a higher voltage position thus slightly lowering its low-signal sensitivity. Rd has risen considerably allowing better impedance matching to the detector coil.
In this next plot we see the impact of changing n from 1 to 2, (from its expected minimum to maximum value). The slope of the log I vs V curve is lower as expected as this is what n represents. The impact is to significantly shift the operating point Vf to higher voltages, above 0.2 in this case. Diode resistance is not significantly impacted, it doubles from129 to 259 kohms. Overall we seek a sharp knee in the curve and this comes with low values on n. Small increases in n have large impact, lowering diode sensitivity.
Keeping n = 1 but increasing Is from 200 to 400 slightly lowers the operating point, Vf going from about 0.1 to just below, maybe 0.09 or so. Rd is cut in half to just 65 kohm. This looks good but recall that at such low Vf you can expect increasing reverse leakage cancelling your sensitivity gains.
These first three plots are designed to give a feel for what impact changing Is or n has on the diode Rd and small-signal sensitivity. Matching the diode to the coil is about more than just choosing the right Is and n of course, its more about the right Rd. Small increases in Is translate to large increases in Rd. Keep n small as you wish a sharp knee for good sensitivity. Small increases in n has a negative impacts on Vf while not buying much in increased Rd.
This plot represents a generic Germanium case. Most germanium diodes I have measured have an Is in the 1000's, n = 1.2 to 1.5, and Rd in the low 10's kohm. They are pretty good diodes for sensitivity, but with low Rd's that don't necessarily match well with the tank. The ITT FO-215 "Holy Grail" diode has an Is = 180 or so and n = 1.05-1.1, and Rd's back in the low 100's kohms similar to many schottky diodes.
Here we have a specific Schottky case, that of the HP 5082-2835. This diode has exceptional qualities with both low Is = 12 and low n = 1.07. Rd for this diode is a good 2306 kohm. One can see from the plot that Vf has moved to a somewhat higher 0.2 V, but the steepness of the curve is still high (n = 1.07) and Rd matches well with the tank coil. Keep in mind that the base case in blue also represents a generic schottky diode with a lower Rd (= 129 kohm) than the 2835. Although the 2835 has a higher Vf, what little it may lose in sensitivity it more than gains in improved matching via a higher Rd.
Finally I present a generic silicon diode case. This diode features very low Is = 6 and a very high n = 1.9. Rd for this case figures to a hefty 8190 kohms. Vf I peg at 0.4V in this case (specific to my plot parameters. More generally the Vf for a silicon diode is about 0.7V). With such a high forward voltage drop this kind of diode is insensitive to any but the strongest local stations.
