Electrical signals can be broadly classified as Alternating Current (AC), where the flow of charge periodically reverses direction, or Direct Current (DC), where charge flows in only one direction. A rectifier is an electronic circuit designed to convert an AC signal into a DC or a pulsated DC signal. This is a fundamental process in power supplies and signal detection systems.

Half-wave Rectifier

A half-wave rectifier produces an output for one half-cycle of the AC input and zero output for the other half-cycle. The op-amp based half-wave rectifier circuit resembles an inverting amplifier with two diodes arranged to control the signal path.

Circuit Operation:

• Positive Half Cycle of Input (): The output of the inverting op-amp attempts to go negative. This forward-biases diode D1, clamping the op-amp output at approximately -0.7V. This voltage is insufficient to forward-bias diode D2, so no current flows to the output resistor. The output voltage is zero volts.
• Negative Half Cycle of Input (): The output of the op-amp goes positive. This reverse-biases diode D1 and forward-biases diode D2. The circuit now behaves as a standard inverting amplifier, and the output voltage is: V_0=-\left(\frac{R_f}{R_1}\right)V_i Since V_i is negative, the output V_0 will be positive.

The final output waveform consists of positive half-cycles that correspond to the inverted and amplified negative half-cycles of the input, while the positive half-cycles of the input are completely removed.

Full-wave Rectifier

A full-wave rectifier produces a positive-going output for both the positive and negative half-cycles of the input signal. The circuit typically uses two op-amps, two diodes, and a network of resistors.

Circuit Operation:

• For the positive half cycle ():
  1. The first op-amp acts as an inverting amplifier. Its output goes negative, which forward-biases diode D1 and reverse-biases diode D2.
  2. The output of the first op-amp is V_{01}=-\left(\frac{R_2}{R_1}\right)V_i.
  3. This signal is fed to the second op-amp, which is configured as an inverting amplifier. The final output voltage is: V_{0}=-\left(\frac{R_5}{R_4}\right)V_{01} = -\left(\frac{R_5}{R_4}\right)\left \{ -\left(\frac{R_2}{R_1}\right)V_{i} \right \} = \left(\frac{R_2R_5}{R_1R_4}\right)V_{i}
  4. The output is a positive, amplified version of the positive input half-cycle.
• For the negative half cycle ():
  1. The first op-amp’s output goes positive. This reverse-biases diode D1 and forward-biases diode D2.
  2. The first stage output is now determined by resistor R_3: V_{01}=-\left(\frac{R_3}{R_1}\right)V_{i}.
  3. This positive signal is fed to the non-inverting input of the second op-amp, which now acts as a non-inverting amplifier. The final output voltage is: V_{0}=\left(1+\frac{R_5}{R_4}\right)V_{01} = \left(1+\frac{R_5}{R_4}\right) \left\{-\left(\frac{R_3}{R_1}\right)V_{i}\right \} = -\left(\frac{R_3}{R_1}\right)\left(1+\frac{R_5}{R_4}\right)V_{i}
  4. Since V_i is negative, the overall output V_0 is positive.

The resulting output waveform is a series of positive half-cycles, representing the rectified version of the entire input signal.

5.2 Clippers

Wave shaping circuits are designed to produce a desired output waveform from a given input, typically by attenuating portions of the wave or altering its DC level. Clippers are a class of wave shaping circuits that remove, or “clip,” a part of the input signal that is either above or below a specified reference level. This is often used to limit the amplitude of a signal or to eliminate unwanted noise spikes.

Positive Clipper

A positive clipper is a circuit that clips the portion of the input signal that is above a positive reference voltage, V_{ref}.

Circuit Operation:

• When : The output of the op-amp tends to be lower than V_{ref}, which forward-biases the diode D1. With the diode conducting, a negative feedback path is established, and the circuit behaves as a voltage follower. Therefore, the output voltage is equal to the input voltage: V_0 = V_i.
• When : The output of the op-amp becomes high enough to reverse-bias the diode D1, breaking the feedback path. The op-amp now operates in an open-loop condition, and the output voltage is limited to the reference voltage applied at the non-inverting terminal: V_0 = V_{ref}.

The resulting output waveform is identical to the input for all voltages below V_{ref}, but is clipped flat at the level of V_{ref} for all input voltages above it.

Negative Clipper

A negative clipper performs the opposite function, clipping the portion of the input signal that is below a negative reference voltage, V_{ref}. The circuit is similar to the positive clipper, but with the polarity of the diode and the reference voltage reversed.

Circuit Operation:

• When : The op-amp output keeps the diode D1 forward-biased. The circuit acts as a voltage follower, and the output tracks the input: V_0 = V_i.
• When : The op-amp output goes low enough to reverse-bias the diode, opening the feedback loop. The output voltage is then limited to the reference voltage: V_0 = V_{ref}.

The output waveform is identical to the input for all voltages above the negative V_{ref}, but is clipped flat at that reference level for all input voltages below it.

5.3 Clampers

While clippers alter the shape of a waveform by removing parts of it, clampers are circuits that shift the entire signal vertically by adding a DC level. The shape and peak-to-peak amplitude of the signal remain unchanged. Clampers are often used in applications where it is necessary to restore a DC level to a signal that has lost it, for example, after passing through a capacitor.

Positive Clamper

A positive clamper is a circuit that shifts the input signal vertically upwards by a positive DC value, determined by a reference voltage, V_{ref}.

Circuit Operation: The input signal is applied through a capacitor-diode network to the inverting terminal, while the reference voltage V_{ref} is applied to the non-inverting terminal. During the first negative half-cycle of the input signal, the diode becomes forward-biased. This allows the capacitor to charge to the negative peak voltage of the input, -V_{peak}. After this initial cycle, the diode remains reverse-biased for the rest of the signal. The capacitor then acts as a DC voltage source with a value of +V_{peak}. The op-amp circuit, configured as a unity-gain buffer for the reference and the capacitor’s stored voltage, adds this DC shift to the incoming AC signal. The resulting output is the original waveform shifted vertically upwards.

Negative Clamper

A negative clamper performs the opposite function, shifting the input signal vertically downwards by a negative DC value.

Circuit Operation: The circuit is similar, but the diode polarity is reversed. During the first positive half-cycle of the input, the diode forward-biases, allowing the capacitor to charge to the positive peak voltage, +V_{peak}. Subsequently, the diode remains reverse-biased. The capacitor now acts as a DC source of -V_{peak} in series with the input signal. The op-amp adds this negative DC level to the input, resulting in the entire waveform being shifted vertically downwards.

5.4 Active Filters

Filters are essential circuits that selectively pass certain frequency components of a signal while rejecting or attenuating others. Passive filters are constructed using only passive components like resistors (R), inductors (L), and capacitors (C). Active filters, on the other hand, incorporate an active element, such as an Op-Amp, in addition to resistors and capacitors. The Op-Amp provides voltage gain and, critically, acts as a buffer with high input impedance and low output impedance. This overcomes the primary drawback of passive filters, which is the loading effect—where the impedance of the next stage alters the filter’s frequency response.

Active Low Pass Filter

An active low pass filter allows low-frequency components to pass through while blocking high-frequency components. The circuit consists of a simple passive RC low pass filter connected to the input of a non-inverting amplifier. This configuration allows the filter’s output to be amplified. The passband gain of the filter is determined by the amplifier’s resistors and is given by \left(1+\frac{R_f}{R_1}\right). If unity gain is desired, the non-inverting amplifier can be configured as a voltage follower.

Active High Pass Filter

An active high pass filter performs the opposite function, passing high-frequency components and rejecting low-frequency ones. Its circuit is constructed by connecting a passive RC high pass filter to the input of a non-inverting amplifier. As with the low pass version, the Op-Amp provides gain, isolation, and a stable output. The passband gain is also \left(1+\frac{R_f}{R_1}\right) and can be set to unity if needed.

Active Band Pass Filter

An active band pass filter allows only a specific band of frequencies to pass, rejecting frequencies that are either too low or too high. This is typically achieved by cascading an active high pass filter and an active low pass filter. The output of the high pass filter is fed into the input of the low pass filter. The high pass filter sets the lower cut-off frequency of the passband, while the low pass filter sets the upper cut-off frequency. The range of frequencies between these two cut-offs is the filter’s passband.

Active Band Stop Filter

An active band stop filter, also known as a band reject or notch filter, blocks a specific band of frequencies while passing all others. This is constructed by combining an active low pass filter and an active high pass filter in parallel. The outputs of both filters are then fed into a summing amplifier. To create the “stop band,” the cut-off frequency of the low pass filter must be set lower than the cut-off frequency of the high pass filter. The summing amplifier combines their outputs, resulting in a signal where only the frequencies within the stop band are attenuated.