Design Goals

Design Description

The precision half-wave rectifier inverts and transfers only the negative-half input of a time varying input signal (preferably sinusoidal) to the output. By appropriately selecting the feedback resistor values, different gains can be achieved. Precision half-wave rectifiers are commonly used with other op amp circuits such as a peak-detector or bandwidth limited non-inverting amplifier to produce a DC output voltage. This configuration has been designed to work for sinusoidal input signals between 0.2mV_pp and 4V_pp at frequencies up to 50kHz.

Design Notes

1. Select an op amp with a high slew rate. When the input signal changes polarities, the amplifier output must slew two diode voltage drops.
2. Set output range based on linear output swing (see A_ol specification).
3. Use fast switching diodes. High-frequency input signals will be distorted depending on the speed by which the diodes can transition from blocking to forward conducting mode. Schottky diodes might be a preferable choice, since these have faster transitions than pn-junction diodes at the expense of higher reverse leakage.
4. The resistor tolerance sets the circuit gain error.
5. Minimize noise errors by selecting low-value resistors.

Design Steps

1. Set the desired gain of the half-wave rectifier to select the feedback resistors.
   ${\mathrm{V}}_{\mathrm{o}}=\mathrm{Gain}\times {\mathrm{V}}_{\mathrm{i}}$
   $\mathrm{Gain}=-\frac{{\mathrm{R}}_{\mathrm{f}}}{{\mathrm{R}}_1}=-1$
   ${\mathrm{R}}_{\mathrm{f}}={\mathrm{R}}_1=2\times {\mathrm{R}}_{\mathrm{eq}}$
   • Where R_eq is the parallel combination of R₁ and R_f
2. Select the resistors such that the resistor noise is negligible compared to the voltage broadband noise of the op amp.
   ${\mathrm{E}}_{\mathrm{nr}}=\sqrt{4\times {\mathrm{k}}_{\mathrm{b}}\times \mathrm{T}\times {\mathrm{R}}_{\mathrm{eq}}}$
   ${\mathrm{R}}_{\mathrm{eq}}\le \frac{{{\mathrm{E}}_{\mathrm{nbb}}}^2}{4\times {\mathrm{k}}_{\mathrm{b}}\times \mathrm{T}\times 3^2}=\left(\mathrm{Enbb}\right)$
   $=\frac{{\left(5.5\times {10}^{-9}\right)}^2}{4\times 1.381\times {10}^{-23}\times 298\times 3^2}=204\mathrm{\Omega }$
   ${\mathrm{R}}_{\mathrm{f}}={\mathrm{R}}_1=2\times 204\le 408\mathrm{\Omega }\to 402\mathrm{\Omega }\text{ (Standard Value)}$

Design Simulations

DC Simulation Results

Transient Simulation Results

200mV_pp at 1kHz

4V_pp at 50kHz

Design References

See Analog Engineer's Circuit Cookbooks for TI's comprehensive circuit library.

See circuit SPICE simulation file SBOC509.

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