Non-linear circuits exhibit a non-linear relationship between input and output.

4.1 Comparators

A comparator compares two input voltages and produces an output indicating which is greater. The output swings between the positive (+V_{sat}) and negative (-V_{sat}) saturation voltages.

• Inverting Comparator: Input is applied to the inverting terminal, and a reference voltage (V_{ref}) to the non-inverting terminal. Output is -V_{sat} if V_i > V_{ref} and +V_{sat} if V_i < V_{ref}.
• Non-Inverting Comparator: Input is applied to the non-inverting terminal. Output is +V_{sat} if V_i > V_{ref} and -V_{sat} if V_i < V_{ref}.
• Zero Crossing Detector: A special case where V_{ref} = 0V. The output switches state as the input signal crosses zero.

4.2 Logarithmic and Anti-Logarithmic Amplifiers

These circuits use the non-linear current-voltage characteristic of a diode in the feedback path.

• Logarithmic Amplifier: Produces an output voltage proportional to the natural logarithm of the input voltage.
  • Output Voltage: V_{0}=-{nV_T}In\left(\frac{V_i}{R_1I_s}\right)
• Anti-Logarithmic Amplifier: Produces an output voltage proportional to the anti-logarithm (exponential) of the input voltage.
  • Output Voltage: V_{0}=-R_{f}{I_{s} e^{\left(\frac{V_i}{nV_T}\right)}}

4.3 Precision Rectifiers

Rectifiers are circuits that convert AC signals to DC or pulsated DC signals.

• Half-Wave Rectifier: An Op-Amp based circuit that produces positive half-cycles at the output for the negative half-cycles of the input, and zero output for the positive half-cycles of the input.
• Full-Wave Rectifier: A more complex circuit, typically using two Op-Amps, that produces positive half-cycles at the output for both the positive and negative half-cycles of the input.