I have seen leaky integrator circuit using a capacitor and resistor in parallel between inverting terminal and the output of an op-amp. But I was wondering if it is possible to make a leaky integrator using switched capacitance integrator.
Electronic – Leaky integrator from Switched capacitor integrator
integrator
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You are correct about the polarity. It should work fine. Can you give some details about the signal you want to integrate? I call that circuit a leaky integrator (or low pass filter) due to R2, so check the time constant for 100nF and 220K (22mS? I'm from the ancient days of uF) versus the rate of change of your signal. This is more an IIR averager than an integrator. Also the gain, which is 1/RC or 1/10. Did you want to divide by 10?
Oh, also change + input to be 100K to ground for input bias balance.
- If I apply at Vin a square wave with an amplitude from -5 V to +5 V, what happens to the voltage on V- node?
In a negative feedback arrangement the amplifier will do its best to keep the - input at the same potential as the + input. The + input is grounded and we refer to the - input as "virtual ground". The voltage there should always be zero unless we drive the output into saturation at which point the feedback won't be able to correct anymore.
- With a regular integrator at the output node I should have a triangular wave that goes from 0V to \$ -V_{in} \times \Large \frac{t}{RC} \$, but in this case what I get at the output? Is it a "rectified"square wave?
simulate this circuit – Schematic created using CircuitLab
Figure 2. (a) and (b) show how the circuit behaves on each alternate clock cycle. (A) and (B) show the result depending on which way the squarewave starts.
Consider the diode operation first: what output voltage will satisfy the virtual ground? Clearly when the input is positve and the output is at -0.7 V (a real diode - not an ideal one) the output will go to -0.7 to maintain 0 V at the - input.
When the input goes negative the diode will be reverse biased so the capacitor will run as a normal integrator and the output will be a triangle wave.
Finally, the output will depend on the starting conditions indicated by diagrams A and B. (Please excuse the arrows. CircuitLab doesn't have a free-style line symbol.
- In A we start with a positive-going square-wave so the output clamps at -0.7 V and the triangle wave continues from there.
- In B we start with a negative-going square-wave so the triangle wave starts and ends at 0 V.
In practice, due to diode and capacitor leakage and any non-symmetry in the square wave the output may settle down somewhere in between the two conditions.
Best Answer
Here's a simple method:
Add a capacitor, \$C_{leak}\$, to your circuit. One terminal is always grounded. The other terminal is connected either to the op-amp's output or to its inverting terminal, alternating between the two at the switching frequency \$f_S\$. This capacitor acts like a resistor of value \$R_{eq}=1/(f_SC_{leak})\$ between the op-amp's output and its inverting terminal.