Frequency response for an integrating LM324

For our experiment we used the following integrator topology:

The frequency response of the circuit can be estimated by neglecting the 100k feedback resistor. This leads to the equation for the unity gain frequency of: Fun = j/2pi*RC. With our values, Fun = j/2pi*100k*1u = 159Hz. The gain will increase by 20dB/dec so at 1.6Hz the gain should be 20dB.

With this topology, at very low frequencies the feedback resistor will start to have an effect on the gain of the circuit, while at very high frequencies the GBP of the op amp will start to effect the circuit. However, with the values used here, the output will be clipped by the swing limits before those factors come into effect.

The true purpose of the 100k feedback resistor in this circuit is to stabilize the output around the CM voltage set by the network connected to the non-inverting input. Without the feedback resistor, the output will start below the swing limit, then rise through the desired output range and past the upper swing limit.

Measured Frequency Response

We did a half-decade sweep from 10Hz to 5kHz to show the frequency response of the circuit.

10Hz	50Hz	100Hz

500Hz	1kHz	5kHz

You can see the output is severely clipped at 10Hz due to the high gain while the output at 5kHz is almost unusable due to switching noise.

The output is 90deg offset from the input through all the measurable readings as expected due to the j in the frequency response equation calculated earlier.

Triangle Wave generation

We used the following circuit to generate a triangle wave from a square wave input.

The formula for calculating the resistor and capacitor values is: Voutp-p = Vin*T/(2R*C). Using the constraints given, it becomes: 3V = 5V*.1ms/(2R*C). We chose a 1uF capacitor so the value of R became (5V*.1ms)/(3V*2uF) =83 ohms.

The output is relatively stable with only minor spikes at the peaks in the sim.

The actual output is bent slightly due to 1u capacitors that we included on the non-inverting network. The circuit would not work without them so we accepted a non-ideal output over no output.