## Quantitative insights into Diode Detector Operation derived from Simulation in SPICE, and some Interesting new Equations relating diode parameters to weak signal sensitivityBy Ben H. Tongue
This Article, #15A, used to be Part 1 of the old Article #17.
The diode detector circuit to which we will refer is shown in Fig. 1. Fig. 1
Assumptions used in the following discussion:
- The Q and L/C ratio of tuned circuit T are assumed to be high and low enough, respectively, so that the 'stored energy effect' of T prevents any appreciable clipping of the positive voltage wave form peak by diode D1.
- The value of C2 is assumed to be high enough so that a negligible amount of RF voltage appears across it.
- The diode parameters Is and n are known from measurement or a Data Sheet. A simplified method of estimating Is is given in Section 2, Article #4, but the parameter n has to be estimated. A method for measuring both Is and n is given in Article #16. The effect of the series parasitic resistance of the diode is assumed to be negligible - as it is at low signal levels for most all detector diodes. Diode back leakage current from either 'parasitic leakage' or operation with voltage swings reaching into the 'reverse breakdown current' region is assumed to be negligible. The diode temperature will be assumed to be 25 degrees C.
- The low power region: Here, the relation between output power and input power approaches 'square-law'. That is, for every one dB change in input power there is about a two dB change in output power. The detector input and output resistances approximate Rx.
- The high power region: Here, the relation between output power and input power approaches 'linear'. That is, for every one dB change in input power there is about a one dB change in output power. The detector input and output resistances are no longer equal. The detector input resistance is equal to about half of R2. The detector output resistance is about twice R1.
- The point where the two areas overlap equally: This is the 'linear-to-square-law crossover point' (LSLCP). At this point there is a 10*log(sqrt2) dB change in output power for every 1.0 dB change in input power (slope of about 1.5). If R1 and R2 are both equal to Rx, in Case A the detector input resistance is about 12% less than Rx and its output resistance is about 12 % greater than Rx.
Most crystal radio sets can deliver a readable signal at an input of Plsc(i) Watts. It would obviously be desirable to lower the input power at which the LSLCP occurs so that more of the weak signals would be closer to the linear mode of operation, experience less insertion power loss and therefore be louder.
At input power levels several times or more below the LSLCP, the impedances of the input and output ports of the detector both approach Rx for both Cases, A and B. At input power levels several times or more above the LSLCP, the detector approaches operation as a peak detector having a low insertion power loss. In this condition the input RF resistance of the detector approaches half the output load resistance and the output resistance of the detector approaches twice the RF source resistance. Case A, the detector input and output ports both approach an impedance matched condition when the signal power is several times lower than that at the LSLCP. At signal power inputs several times greater than that at the LSLCP, a moderate impedance mismatch exists at both the input and output ports. In Case B, conversely, the detector input and output ports are both are moderately impedance mismatched when the signal power is several times lower than that at the LSLCP. At signal power inputs several times greater than that at the LSLCP, both input and output ports approach an impedance matched condition.
Unpublished information from Xavier Le Polozec indicates that the optimum practical compromise values for R1 and R2, for
The following equations are developed for the Class A termination condition of
Differentiating the Shockley diode equation with respect to the diode junction voltage yields:
Some obvious relations:
Some simple manipulation of equations (0) and (2) results in the relation: V2lsc(o)=0.051*n Volts (2a)
A proper relation between Po, Pi and I2 obviously requires that I2 approach zero as Po/Pi approaches zero, that Po/Pi approach proportionality to I2 as I2 becomes low (the square law relation) and that Po approach Pi as I2 becomes very high. Also, at an output power of Plsc(o), I2 must equal 2*Is, as stated earlier. Interesting note: Since, at the LSLCP, I2=2*Is (eq. 1),
Substituting the value of Plsc(o) from equation 2 into equation 4 results in:
A lot of mathematical manipulation of the relations given above results an equation that fits the simulation data quite well over the whole range of the graph in Fig. 2.
A rearrangement of the terms in equation (5) yields:
From equation (5r), at low output power power levels, the input power required to produce a given output approaches:
Prearranging terms of equation 5Li:
An equation that fits the detector
Adjust the DC component of the diode load to equal its axis-crossing resistance (0.0256789*n/Is ohms).** Measure the DC voltage V2 developed across the DC load. Some simple manipulation of equation (3) above results in equation (7).
** See articles #16 and #27 for info on determining the Is and n of diodes as well as measurements on some diodes.
ultimate very weak signal sensitivity. If all other diode parameters are kept the same, the input and output resistances of a diode detector are directly proportional to n and inversely proportional to Is. 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 new impedances are doubled). The result will be a detector insertion power loss change of: 10*log(oldn/newn) dB. That is, weak signala doubling of n will result in a 3 dB increase in insertion power loss, assuming the input power is kept the same and input and output impedances are re-matched. The result is a 3 dB reduction of output power (volume). A similar effect occurs if Is of the diode is increased except that this change reduces the impedances that must be re-matched instead of increasing them.
Interesting note: A simple manipulation of Equations #0, 2 and 4 shows that, at the LSLCP, the RMS value of the AC signal at the input to the diode is: (0.08895*n) Volts, and it is independent of Is. One final equation: One can combine two equations: Let us review the conditions that apply to equation (8) before discussing it.
that of one original diode.
twiceExperimental measurements on eleven different diodes used as detectors is shown in Article #27. Close correlation between these equations and actual measurements is demonstrated. #15A Published: 04/10/2001; Revised: 12/07/2008 |