# New ways to Increase Diode Detector Sensitivity to Weak Signals, and a way to determine if a diode detector is operating above or below its Linear-to-Square-Law Crossover Point

By Ben H. Tongue

Quick Summary:  The very low signal sensitivity of a crystal radio set can be improved by cooling the diode. This possibility arises when the rectified DC current is below about twice the Saturation Current of the diode. Also see Article #28 for more info on increasing weak-signal sensitivity.

Definitions of terms to be used:

Plsc(i)    Input power at the linear-to-square-law crossover point
Plsc(o)   Output power at the linear-to-square-law crossover point
Is           Saturation current of the diode
n            Ideality factor of the detector
DIPL     Detector insertion power loss
Pi          Available input power
Po         Output power
sqrt       Take the square root of the expression following
C          Temperature in degrees Celsius
Ri          Detector input resistance
Ro         Detector output resistance
R1         Source resistance
I2          Rectified current
Rxc       Slope of voltage/current curve of a diode at the origin (axis-crossing resistance).   Rxc=0.02568*n/Is, at 25° C.
Kt         Temperature in ° Kelvin
S11       A measure of input impedance match.  S11=20*log|[(|Ri-R1)/(Ri+R1)]|
SPICE
A circuit simulation computer program.  ICAP/4 from Intusoft was used in all simulations.

The old Article #17 has been separated into two Articles.  This new Article #17A is a revision of Part 2 of the old #17.  Part 1 has been broken out and renamed "Quantitative Insights into Diode Detector Operation Derived from Simulation in SPICE, and some Interesting new Equations.".  It is numbered15A.

Assume that a station one can barely read has a power sufficient only to operate the detector at or below the "Linear-to-square law crossover point" (LSLCP).  This is the point where the rectified diode DC current is about twice Is.  Volume can be increased if the Plsc(i) point could be shifted to a lower RF power level.  This will result in less insertion power loss since operation will now be closer to the linear region.  The RF power required to operate a diode detector at its Plsc(i) point (at 25° C.) is shown as equation (4a) in Article #15A.  It can be rewritten as:

Plsc(i)=0.0010341*Kt*Is*n  Watts    (1)

When referring to the schematic of a diode detector, Figure 1 will be used.

Fig. 1

Diode Detector Output and Insertion Loss vs. Input Power.  The LSLCP
is shown by the black arrow.

 Fig. 2 - A SPICE simulation of the relation between output and input power. Fig. 3 - Data from a SPICE simulation showing  detector insertion power loss vs. input power.

It is assumed that input and output are impedance matched.  One can see from equation (1) that if Is, Kt or n can be lowered, the Plsc(i) point is lowered and therefore, the volume from weak signals can be increased.  The reciprocal of the product of Is, n and Kt can be seen to be a sort of "weak signal diode figure of merit" (WSDFM).  It has been shown that in all semiconductor diodes, a small % drop in Kt will result in a much larger % drop in Is from its initial value.  It must be remembered that the reduction of Is or Kt increases Ri and Ro.  If n is reduced, Ri and Ro are reduced.  Re-matching of impedances (Ri and Ro) is required to gain the benefits being sought.

• Reduction of Is:  The main limit to using a diode of a lower Is has to do with the resultant increase in RF input (Ri) and audio output (Ro) resistances of the detector.  Practical low loss RF and AF impedance matching will be a problem.  At input signal levels at or below the Plsc(i) point, those values are about: Ri = Ro = 0.00008614*n*Kt/Is ohms.  The example in Figs. 2 and 3 are for a case where Ri and Ro are both about 700k ohms, using a diode with an Is of 38 nA and an n of 1.03.  This is close to the limit of practicality and applicable mainly to crystal radio sets using a single tuned, high inductance, high Q loop antenna with a high quality, high transformation ratio audio transformer.  A practical maximum value for R2 for most high performance crystal radio sets designed for use with an external antenna is about 330k ohms.  This requires a diode with an Is of about 80 nA instead of 38 nA, for a good impedance match.  The higher Is of the diode increases Plsc(i)  by about 3 dB and that reduces the output of signals that are well into the square law region by about 3 dB.  Signals well above the LSLCP are hardly affected at all.  Note that "production process variation" of Is is usually rather great.  This approach is practical and just requires selecting a diode type having the optimum Is.  Simple as that, no mumbo-jumbo. See Table 1 in Article #27 for measured Is values of several diode types.  Keep in mind that some diode types can be damaged by static electricity. If the diode is not destroyed, it's reverse leakage current gets elevated, ruining weak signal sensitivity.  Usually, diodes that have low values of Is also have a low reverse breakdown voltage, increasing their susceptibility to static electricity damage.
• Reduction of n:  The value of n does not vary as much as does Is among diodes of the same type.  Schottky diodes designed for detector use usually have a low value for n.  N can range between 1.0 and 2.0.  Probably so called 'super diodes' have a low n and their values of Is and n are such that a good impedance match is realized in the particular crystal radio set used.  The use of a diode with a reduced n not only reduces Plsc(i), but also reduces Ri and Ro, a reverse effect than that from reducing (Is).  Most diode types rated for use as detectors or mixers usually have a low n.
• Reduction of Kt:  The temperature of any diode can be lowered by spraying it with a component cooler spray (221 degrees K.) every so often.  A longer lasting, but lesser cooling effect can be had if the diode is placed crosswise through two diametrically opposite small holes in a small housing (such as a 1'' dia. by 2.5 inch long plastic pill container) with a stack of old style copper pennies in the bottom to act as a thermal mass.  This assembly is used after being cooled in a home freezer to about 0 degrees F. (255 degrees K.).  It is then taken out and connected in the crystal radio set.  An even lower temperature can be attained if some pieces of dry ice (195 degrees K.) are substituted for the pennies.  The problem with reducing Kt is that (Is) is very temperature sensitive, so it also changes.  Agilent states in App. note #1090 that the junction resistance of HSMS-2850 Schottky diode increases 100 times for a 70 degree K. reduction in temperature.  That indicates a much greater % change in (Is) than in degrees Kelvin temperature.  A 70 degree K. temperature drop may reduce the Is by 100 times, raising Ri and Ro by 100 times.  That ruins impedance matching and increases loss greatly (the signal goes away).  The answer is to experimentally try diodes that have a high Is at room temperature (298 degrees K.), that will drop to the correct value at the reduced temperature.  One candidate is the Agilent HSMS-2850 (room temperature Is = 3000 nA).  Another is a 2N404A Ge transistor with the base and collector leads tied together (room temperature Is = 1500 nA).  Most modern diodes sold as 1N34A have (Is) values ranging from about 200 to above 600 nA.  Measurements show that for germanium or non-zero-bias type silicon Schottkys, a 10 degree C (18 degree F.) change in temperature will result in an approximately two times change in Is.  Other measurements show that with zero-bias-type Schottkys, a 14 degree C. (25 degree F.) change in temperature will result in approximately a two times change in Is.  This approach is not practical since the desired results can be attained by selecting a diode type having the required Is at room temperature.

The ideality factor (n) 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 power loss change (weak signals only) of: 10*log(oldn/newn) dB.  That is, a doubling of n will result in a 3 dB increase in insertion power loss, assuming the input power is kept the same.  This illustration shows the importance of a low value for n.

Warning: Don't use two diodes in series if you want the best weak signal sensitivity.  The result of using two identical diodes in series is the simulation of an equivalent single diode having the same Is but an n of twice that of one original diode.

A diode detector is operating at its LSLCP (usually with about a 5 dB insertion power loss), if the average rectified DC voltage across the resistive component of its load is (n*51) mV (See Article #15 for a discussion of this).  When checking this, use a large enough bypass capacitor across the DC load to maximize the voltage.  If one doesn't know the n of one's diode detector, it can usually be assumed to be about 1.07.  A requirement for the (n*51) mV relation to be correct is that the detector be approximately impedance matched at its input for RF and accurately matched at its output for DC and audio.  Specifically, the DC load resistance must be set to 0.026*n/Is ohms (see Part 4 of Article #0 for info on n and Is).  See Fig. 5 in Article #26 for a typical method of adjusting the DC resistance of the diode load and monitoring the rectified voltage.  Typical values for n and Is for many diodes may be found in Articles #16 and 27.  The audio load AC impedance matching requirement is not very important if one is interested only in hearing the volume delivered from ones headphones when the diode is operating at its LSLCP.  The reason is that volume is a slow and gradual function of audio mismatch, for moderate mismatches.  A two-to-one audio mismatch causes a loss in audio output of only 0.5 dB.  A four-to-one mismatch causes a loss of 1.9 dB (hardly audible).

#17A  Published:  04/10/01;  Revised 11/29/2006
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