RC Integrator and Differentiator using QUCS

Dr. Hari V S
Department of Electronics and Communication
College of Engineering Karunagappally

What You will Learn

• You will understand the operation of simple integrator and differentiator circuits using QUCS
• You will learn the frequency response characteristics of integrator and differentiator by dint of ac simulation.

Theory

Differentiator is a high pass circuit that produces the time derivative of the input signal at the output. The circuit is shown below.

\begin{equation} \nonumber v_{o}=I_{o}R=RC\frac{d(v_{s}-v_{o})}{dt}\\ \approx RC\frac{dv_{s}}{dt} \end{equation} Integrator is low pass circuit that generates the integral of the input signal. In the simple integrator circuit below. For the integrator, \begin{align} \nonumber v_{o}&=\frac{1}{C}\int i\,dt\\ &\approx \frac{1}{RC}\int v_{s}\,dt \end{align}

Design

For the differentiator, $RC < 0.0016T$ where T is the period of the input signal. Let T be 1mS and C be 0.001 $\mu$F. Then R ≈ 1.5K
For the integrator, $RC > 16T$ . Let T be 1mS and C be 1 $\mu$F. Then R ≈ 15K

Experiment

Launch QUCS. Go to Components in the left pane and select the item Lumped Components. Drag and drop a resistor and capacitor onto the schematic window. Wire them up as in the circuit of differentiator.

Change the properties of both components to match the differentiator in the above figure.

Drop 1mS square wave source ( Components → Sources ) of 1 V peak to peak amplitude onto the schematic window.

Double click on the wire segments between source and capacitor and capacitor and resistor and name these probes as vs and vo respectively.

Drop transient simulation ( Simulations → Transient simulation ) and change the properties to fit the schematic below.

Also insert the equation ( Insert → Insert Equation ) to get the equation for voltage gain in the schematic.

Press F2 to run the simulation. Observe the .dpl winow for input and output waveforms as shown below.

Replace the transient simulation from the schematic with ac simulation . Change its properties as in the schematic below.

Observe the frequency response and the 3-dB frequency.

Repeat the above steps for the integrator with the schematic and the resulting signals, shown below.

Repeat the steps for plotting the frequency response of the integrator with the schematic and the resulting response, shown below.

Observe the frequency response and the 3-dB frequency.

What You Learned

• You understood the theory, design and operation of simple integrator and differentiator circuits using QUCS
• You understood the frequency response characteristics of integrator and differentiator by dint of ac simulation.
• You understood the frequency response of simple RC circuits.