There are many applications for precision rectifiers, and while most are suitable for use in audio circuits, I thought it best to make this the first ESP Application Note. While some of the existing projects in the audio section have a rather tenuous link to audio, this information is more likely to be used for instrumentation purposes than pure audio applications.
Typically, the precision rectifier is not commonly used to drive analogue meter movements, as there are usually much simpler methods to drive floating loads such as meters. Precision rectifiers are more common where there is some degree of post processing needed, feeding the side chain of compressors and limiters, or to drive digital meters.
There are several different types of precision rectifier, but before we look any further, it is necessary to explain what a precision rectifier actually is. In its simplest form, a half wave precision rectifier is implemented using an opamp, and includes the diode in the feedback loop. This effectively cancels the forward voltage drop of the diode, so very low level signals (well below the diode's forward voltage) can still be rectified with minimal error.
The most basic form is shown in Figure 1, and while it does work, it has some serious limitations. The main one is speed - it will not work well with high frequency signals. To understand the reason, we need to examine the circuit closely. This knowledge applies to all subsequent circuits, and explains the reason for the apparent complexity.
Figure 1 - Basic Precision Half Wave Rectifier
When the input signal becomes positive again, the opamp's output voltage will take a finite time to swing back to zero, then to forward bias the diode and produce an output. This time is determined by the opamp's slew rate, and even a very fast opamp will be limited to low frequencies - especially for low input levels. The test voltage for the waveforms shown was 20mV at 1kHz. Although the circuit does work very well, it is limited to relatively low frequencies (less than 10kHz) and only becomes acceptably linear above 10mV or so (opamp dependent).
Note the oscillation at the rectified output. This is (more or less) real, and was confirmed with an actual (as opposed to simulated) circuit. This is the result of the opamp becoming open-loop with negative inputs. In most cases it is not actually a problem.
Figure 2 - Rectified Output and Opamp Output
The circuit is improved by reconfiguration, as shown in Figure 3. The additional diode prevents the opamp's output from swinging to the negative supply rail, and low level linearity is improved dramatically. A 2mV (peak) signal is rectified with reasonably good linearity. Although the opamp still operates open-loop at the point where the input swings from positive to negative or vice versa, the range is limited by the diode and resistor. Recovery is therefore a great deal faster.
Figure 3 - Improved Precision Half Wave Rectifier
Figure 4 shows the standard full wave version of the precision rectifier. This circuit is very common, and is pretty much the textbook version. It has been around for a very long time now, and I would include a reference to it if I knew where it originated. The tolerance of R2, 3, 4 and 5 is critical for good performance, and all four resistors should be 1% or better. Note that the diodes have been reversed to obtain a positive rectified signal. The second stage inverts the signal polarity. To obtain improved high frequency response, the resistor values should be reduced.
Figure 4 - Precision Full Wave Rectifier
The Alternative (Analog Devices)
A little known variation of the full wave rectifier was published by Analog Devices, in Application Brief AB-109 . In the original, a JFET was used as the rectifier for D2, although this is not necessary if a small amount of low level non-linearity is acceptable. The resistors marked with an asterisk (*) should be matched, although for normal use 1% tolerance will be acceptable.
Figure 5 - Original Analog Devices Circuit
For most applications, the circuit shown in Figure 6 will be more than acceptable. Linearity is very good at 20mV, but speed is still limited by the opamp. To obtain the best high frequency performance requires a very fast opamp, and reduce the resistor values.
Figure 6 - Simplified Version of the AD Circuit
Figure 7 - Original Intersil Precision Rectifier Circuit
This gives a transfer function of ...
Gain = 1 / ( 1 + (( R1 + R2 ) / R3 )) ... 0.5 with the values shown above1V input will therefore give an output voltage of 0.5V. During this positive half-cycle of the input, the diode disconnects the op-amp output, which is at (or near) zero volts. Note that the application note shows a different gain equation which is incorrect. The equation shown above works.
During a negative half-cycle of the input signal, the CA3140 functions as a normal inverting amplifier with a gain equal to -( R2 / R1 ) ... 0.5 as shown. Since the inverting input is a virtual earth point, during a negative input it remains at or very near to zero volts. When the two gain equations are equal, the full wave output is symmetrical. Note that the output is not buffered, so the output should be connected only to high impedance stage, with an impedance much higher than R3.
Figure 8 - Modified Intersil Circuit Using Common Opamp
Note that the input impedance of this rectifier topology is non-linear. The impedance presented to the driving circuit is 30k for positive half cycles, but only 10k for negative half-cycles. This means that it must be driven from a low impedance source - typically another opamp. This increases the overall complexity of the final circuit.