As shown, the diode passes positive half waves and blocks negative half-waves. But, what happens if the input signal is only 0. Rectification never occurs because the diode requires 0. Even if a germanium device is used with a forward drop of 0. Even if the signal is large enough to avoid the forward voltage drop difficulty, the source impedance must be relatively low. At first glance it seems as though it is impossible to rectify a small AC signal with any hope of accuracy.
One of the items noted in Chapter 3 about negative feedback was the fact that it tended to compensate for errors. Negative feedback tends to reduce errors by an amount equal to the loop gain. This being the case, it should be possible to reduce the diode's forward voltage drop by a very large factor by placing it inside of a feedback loop.
To a first approximation, when the input is positive, the diode is forward-biased. In essence, the circuit reduces to a simple voltage follower with a high input impedance and a voltage gain of one, so the output looks just like the input.
On the other hand, when the input is negative, the diode is reverse-biased, opening up the feedback loop. No signal current is allowed to the load, so the output voltage is zero. Thanks to the op amp, though, the driving source still sees a high impedance. Due to the effect of negative feedback, even small signals may be properly rectified.
In order to create the circuit output waveform, the op amp creates an entirely different waveform at its output pin. For positive portions of the input, the op amp must produce a signal that is approximately 0. This extra signal effectively compensates for the diode's forward drop. Because the feedback signal is derived after the diode, the compensation is as close as the available loop gain allows.
At low frequencies where the loop gain is high, the compensation is almost exact, producing a near perfect copy of positive signals. When the input signal swings negative, the op amp tries to sink current in response. As it does so, the diode becomes reverse-biased, and current flow is halted. At this point the op amp's noninverting input will see a large negative potential relative to the inverting input. The resulting negative error signal forces the op amp's output to go to negative saturation.
Because the diode remains reverse-biased, the circuit output stays at 0 V. The op amp is no longer able to drive the load. This condition will persist until the input signal goes positive again, at which point the error signal becomes positive, forward-biasing the diode and allowing load current to flow.
This time is determined by the device's slew rate. Along with the decrease of loop gain at higher frequencies, slew rate determines how accurate the rectification will be. Suppose that the op amp is in negative saturation and that a quick positive input pulse occurs.
In order to track this, the op amp must climb out of negative saturation first. If only slow signals are to be rectified, it is possible to configure the circuit with moderate gain if needed, as a cost-saving measure. Finally, for negative half-wave output, the only modification required is the reversal of the diode.
The circuit is shown redrawn with the nodes labeled. This example utilizes the op amp model examined earlier. This circuit also has another limitation. The input impedance is determined by the input resistor R1. R1 usually has a limited value, thus the circuit must be driven from a low-impedance source. The op-amp shown in Fig. You could switch inputs on the op amp to turn it into a non-inverting amplifier, but the phase difference comes in handy if you want to build a precision full-wave rectifier.
The typical waveforms of the circuit of Figure 1, are shown on figure 2b. The input frequency is Hz. An extremely simple half-wave precision rectifier. At this point, one might ask if it is possible to build a simpler precision rectifier which will use only one diode. The answer is that such a basic configuration exists and it looks like the circuit presented on figure 3. This basic configuration has a problem so it is not commonly used.
When the input becomes even slightly negative, the operational amplifier runs open loop, as there is no feedback signal through the diode. With a typical high open loop gain operational amplifier, the output saturates.
If the input then becomes positive again, the op-amp has to get out of the saturated state before positive amplification can take place again. This change generates some ringing and takes some time, greatly reducing the frequency response of the circuit.
Figure 3. Basic half-wave precision rectifier. Turning a half-wave precision rectifier circuit into a precision full-wave rectifier.
We can turn a half-wave precision rectifier circuit into a precision full-wave rectifier by using a weighted inverting summer, as shown in figure 4, but a bit of thought has to go into picking the summing resistors.
As shown in Fig. Figure 4. Full-wave precision rectifier by using a weighted inverting summer. If R1 and R3 in Fig. In other words, the net result would be a voltage of zero. We can solve that problem by mixing in twice the half-wave voltage. Based on the concept described above about turning a half-wave precision rectifier circuit into a precision full-wave, we may combine the circuits on figures 1 and 4, in order to make a two stages op-amp full wave precision rectifier.
The resulting topology, is shown on figure 4b:. In the circuit of figure 4b, we're adding the original AC signal and the output of an arbitrary gain half-wave rectifier.
This is somehow different from the case of figure 4, when we assumed that the half-wave DC input was connected to a unity-gain half wave rectifier. Since R1 and R2 give the gain for the first stage and R3 and R5 for the second stage, in order to make the circuit to behave as a full wave rectifier, we must get the same amplitude for both cycles.
R6 is added to minimize the error caused by the input bias current. The circuit in Figure 4b has a good linearity, down to a couple of mV at low frequencies, but the high-frequency response is limited by the op amp bandwidth as always. Full-wave rectification can also be achieved by inverting the negative halves of an input-signal waveform and applying the resulting signal to another diode rectifier.
The outputs of the two rectifiers are then joined to a common load. This idea is described in figure 5. The waveforms at various nodes are also shown in the same figure.
For example, in instrumentation applications, the signal to be rectified can be of very small amplitude, say 0. Also the need arises for very precise transfer characteristics. Precision Half-Wave Rectifier- The Superdiode There are many applications for precision rectifiers, and most are suitable for use in audio circuits.
A half wave precision rectifier is implemented using an op amp, 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 main one is speed. It will not work well with high frequency signals. The forward voltage is effectively removed by the feedback, and the inverting input follows the positive half of the input signal almost perfectly. This time is determined by the op amp's slew rate, and even a very fast op amp will be limited to low frequencies. Exercise The diode has a 0. Assume that the op amp is ideal and the voltage drop changes by 0.
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