Detector Noise

Backing up a bit, if you're trying to build a low noise diode detector, it might be a good idea to investigate using one of those 'ideal diode' op-amp circuits along with a low noise op-amp and (if you can find such a beast) a low noise diode.

There are pico-amp (ultra low) leakage diodes. I assume that low leakage might provide low noise. They're certainly used in applications that demand low noise. (For some inexplicable reason, I've got buckets of them in my junk box.)

Most AM detectors are used in AM radios in the LF, MF, and HF bands. In these cases the overall noise level is set by the external environment.

If you're building something for higher frequencies, then the noise level is set by the first RF amplifier stage and following stages really don't matter (as much).

So, for most real world applications, wouldn't it be easier to determine what SNR you need in the detector (say 100dB) and then simply prove the SNR of the detector is WAAAY better than required?

Sorry I can't help with the Spice AC noise analysis. Never gone that deep with Spice.

Some pico amp diodes are actually junction fets with the drain or source lead cropped off and specially tested for low IGSS.

What that may or may not do to the noise I really don't know... and the datasheets I've just consulted have no noise spec at all...

"Low leakage" diodes won’t give low noise because they typically have higher series resistance. In principle any diode will have similar shot noise providing the series resistance is low and the ideality factor is close to unity.

Low leakage "Diodes" like JPAD5 series which are FETs would probably be horrible as detectors due to their high series resistance. However unless it is quantified then there is no way to say for sure.

I would think that people in the comms business would have a way of estimating the noise caused by a detector circuit. The noise of the detector only becomes negligible when it is say 10x lower than the noise from the received signal. If you don’t know how large the detector noise is then how do you know when you have amplified the RF signal enough (from a theoretical point of view)? I'm not in the comms business myself which excuses my ignorance (to some extent).

I’m thinking that the noise in the diode is ‘sampled’ by the carrier current pulses, that is by the current spikes that occur at the carrier frequency. The voltage noise should be least at the highest current values so I would think that the noise should be due to the peak currents in the diode, rather than the mean current. The detector circuit itself will effectively filter out the carrier ‘sampling spikes’ leaving a baseband noise waveform due to the peak currents in the diode. In order to estimate the peak current in the diode I would have to assume a conduction angle in the diode and note the load current due to the resistor//capacitor. If the output voltage were say 0.4V across 1M then the resulting 0.4µA mean current would translate to perhaps 10x as much as a peak current. That’s still only 4µA. I get the noise as 10nV/sqrt(Hz) for that case, which doesn’t sound too bad.

The first circuit logbook describes sounds like a linear detector, but the second is the square law. As a diode bias ccurrrent increases so does the shot noise (as stated above),and so does the flicker noise but the diode's dynamic resistance decreases. I am reading from Dennis D. Vaccaro's "Electronic Warfare Receiveing Systems". The tangential sensitivity increases as the bias current increases but gradually the noise dominates the output, and so the TSS starts to go down.
So you are interested in one of the noise terms, but it may be the system detection performance you really want to understand and optimize.

In your second post you mention the peak current and the conduction angle. In a small signal detector (square law) the conduction angle does not exist. The didode should never really turn on, you are riding along the curve. The peak current should not vary very much, the signal should vary the current very little relaive to the bias current, you are riding the curve along a verysmall section, thus the small signal definition of the square law. So the mean current should epresent the peak current and the minimum very well.
Since the curve you are riding is not straight (it is cuved like a parabola or a square law term) the sine wave variation input even though small gets squared. Squaring a sine wave produces a DC and a double frequency sine wave term. The double frequency term gets filtered by the capacitor you mentioned. The DC is what you are interested in. The 1M Ohm is part of the low pass filter, the capacitor should bleed very little at the high frequencies, but very little DC (or the audio near DC).

Visigoth,
both circuits are square law detectors; it is just a question of applied signal level. Both are square law detectors up to about -20dBm. This part is easy to simulate as a SPICE transient simulation. Likewise the current in the diode simulates well and is appropriately peaky as I suggested in my earlier post. Provided the forward and reverse recovery times of the diodes are faster than the incoming cycle time, the diode behaves as a rectifier.

Your quote from Vaccaro "The tangential sensitivity increases as the bias current increases but gradually the noise dominates the output, and so the TSS starts to go down." is of interest.

Is he putting a DC bias through the detector diode or is he talking about the DC output level increasing (self-bias) as the input signal increases?

The small signal below -20 dBm should produce a voltage that does not exceed either the end of the square law at 0.6V or so for Si or near zero volt (otherwise rectification occurs).
If you are rectifying by crossing the region between conduction and non conduction, then you are not in the square law region.
If you have some of the noise as shot noise, and you allow the tails to exist (very high currents) even if infrequently, those currents do not have to obey the diode devices rectification rules.
A fast diode is nice because the capacitance is less (in general), not because the fast diode also happens to be able to have its charge swept out quickly when the voltage reverses in rectification. Again, I am repeating the point that a diode used in its square law detection region should not be rectifying by crossing the voltage sign reversal region.

As your bias current increases you get two benefits. First, you move further from the rectification region allowing the small signal to cross that boundary, and second, the diodes dynamic Z is lower. The resistive component may be near 50 k Ohm, but since it is square law the nominal Z changes with the bias point. But increasing the current increases both your flicker and shot noise. So, there may be an optimum you can find for a particular detection level you desire.