Several articles on this site have used diode half wave detectors down to very low signal levels, well below the commonly perceived ‘threshold' of the diodes, and it has prompted comments to the effect that this cannot work.

## Really simple PN junction diode model

An ideal diode is a device that conducts in one direction with zero voltage drop, and does not conduct in the other direction.

Practical diodes typically have an IV characteristic with a knee at some small forward bias from about 0.2V to 0.6V depending on the nature of the PN junction.

An often used simple model of a practical diode is an ideal diode with a series battery of voltage equal to the offset of that knee, the ‘threshold' if you like.

This model may be quite adequate when the applied voltage is much larger than the knee voltage, eg if you were rectifying 24V AC.

## Practical diodes

### Shockley's diode equation

William Shockley modelled the IV characteristic of a diode as \(I_D=I_S(e^{\frac{V_D q}{n k_B T }}-1)\) where I_{D} is the diode current, I_{S} is the reverse-bias saturation current (or scale current), V_{D} is the voltage across the diode, k_{B} is Boltzman's constant, T is absolute temperature, q is an elementary charge, and n is the ideality factor, also known as the quality factor or emission coefficient.

\(\frac{k_B T }{q}\) is often known as V_{T}.

Shockley's equation with n=1 is often known as Shockley's ideal PN diode.

### BAT46

Let's look at the BAT46 Schottky diode, it has PIV=100V and is very suited to a lot of these higher voltage RF signal projects.

Above is the IV characteristic from a datasheet. They are often not very helpful at really low currents as used in some of these applications, but note the great temperature sensitivity.

Above is measurement of a sample BAT46 using a DCAPRO component tester. The plot is on log axis and an exponential curve fit is performed to extract Shockley's coefficients.

V_{T}=0.025852, Is can be read directly as 71nA, n=1.064.

So, the BAT46 is close to Shockley's theoretical equation, and it is a far better characterisation than the really simple diode model.

## Half wave detector model

A commonly used circuit in RF detectors is a half wave detector.

Modelling circuit behavior at small RF signal levels calls for factoring in source impedance, diode behavior at RF (ie its self capacitance), non-ideal behavior of the filter capacitor etc.

Above is a simple half wave detector circuit modelled in LTSPICE. The current source and 50Ω load represent a current transformer and burden, but results would be the same for an equivalent voltage generator and series 50Ω resistor.

The current specified is 0.002 Apk, and the voltage developed across the 50Ω resistor is approximately 100mVpk.

Above is a plot from the simulation showing the voltage across the 50Ω resistor (0.1mW) in red, the voltage across the diode in blue, the voltage across the 10kΩ load in cyan, and the diode current in green.

Even though the input voltage to the detector is well below the notional threshold of the diode, the DC value of the output voltage is 7.4mV which is measurable using the ADC in the referenced project.

Studying the four waveforms, their magnitude and timing relationship, is informative and might challenge readers previous understanding of this fairly ubiquitous circuit. The red trace is almost a perfect sine wave, the others are less so.

So, we note that even for a very small sinusoidal input voltage to the half wave detector, we have derived DC output component, albeit quite small and with some residual ripple (though the ripple wave shape might not resemble the triangular wave usually assumed).

The next problem is to calibrate a meter given that the half wave detector response is not simply linear at very small input voltages.

## Meter calibration

A set of measurements were made of Prf vs Vdc at the ADC pin for power from 1 to 25W. One outlier was discarded.

The tabulated data which was imported to Veusz to perform a second order polynomial curve fit.

Above is the curve fit (on log-log axes) of power vs Vdc.

One approach to calibrating an analogue meter is to simply make marks on the scale at appropriate points with labels to suit. The graphic above is for a dual range RF current probe and it can be seen that whilst the 1000mA range is approximately linear, the 100mA range is quite compressed, more so at lower values.

The reference project used a microcontroller and digital display, so that opens up the possibility of transforming measured Vdc to indicated power using the calculating power of the microcontroller, and the curve fit deduced above is one way in which that can be done, see the equation in the graph legend.

Another approach is that used at Digital display for half wave detector with cubic spline interpolation – part 1.

## Conclusions

A practical PN diode does not simply fail to conduct for applied voltages less than its ‘threshold' or knee voltage.

The Vout/Vin response of the common half wave detector circuit becomes quite non linear for Vin less than about 5 times the knee voltage, but that response can be incorporated in one of many ways to make a useful instrument.

The technique does work, but it appears there are some hams who are so confident in their knowledge that they will not challenge that knowledge by trying the technique.