Integrating operational amplifier

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maven sharma
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Homework Statement


Calculate the output voltage of the amplifier
Hand-drawn schematic of an inverting op-amp circuit with input resistor R1 from V_INPUT to the inverting terminal, and feedback branch of resistor R2 in series with capacitor C1 from the output back to the inverting input; non-inverting input grounded, output labelled V_output voltage, with the caption Calculate output voltage.

2. Homework Equations
Schematic of an inverting integrator op-amp: input V_IN feeds through resistor R to the inverting input, with capacitor C in feedback from output V_OUT; non-inverting input grounded.
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https://www.electronics-tutorials.ws/opamp/opamp32.gif

The Attempt at a Solution


I do not know how to approach a circuit with RC in series to inverting terminal of integrating op amp
 
Attachments
  • Hand-drawn op-amp circuit: input V_INPUT voltage through Resistor (R1) to the inverting terminal, with Resistor (R2) in series with capacitance (C1) in feedback to Vout; non-inverting input grounded; labels Ao and V_output voltage.
    upload_2018-5-2_16-29-21.jpeg
    20.8 KB · Views: 832
  • Hand-drawn schematic of an inverting op-amp circuit with input resistor R1 from V_INPUT to the inverting terminal, and feedback branch of resistor R2 in series with capacitor C1 from the output back to the inverting input; non-inverting input grounded, output labelled V_output voltage, with the caption Calculate output voltage.
    lWWX9.jpg
    14.5 KB · Views: 1,345
  • Schematic of an inverting integrator op-amp: input V_IN feeds through resistor R to the inverting input, with capacitor C in feedback from output V_OUT; non-inverting input grounded.
    classic_circuit_1000-jpg.jpg
    12.2 KB · Views: 1,164
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Discussion

maven sharma said:
I do not know how to approach a circuit with RC in series to inverting terminal of integrating op amp
You still write the KCL equation at the "-" input to the opamp. The impedance to the right is just the sum of the impedances of the resistor and capacitor. Can you show us that equation and then how you would solve it to get Vo/Vi? :smile:
 
berkeman said:
You still write the KCL equation at the "-" input to the opamp. The impedance to the right is just the sum of the impedances of the resistor and capacitor. Can you show us that equation and then how you would solve it to get Vo/Vi? :smile:
Handwritten-style slide deriving the output of an integrating op-amp circuit using KCL: 0 = U1/R + C dU2/dt = Uin/R + C dUout/dt, ending with Uout = -(t/RC) Uin, beside a schematic with input resistor, feedback capacitor and op-amp.


yeah i can do it when its standard integrating op amp circuit but when a resister ans capacitor is added(see below image) to the inverting terminal in feedback then i don't know how to form equation
Hand-drawn op amp circuit: input voltage V_INPUT through Resistor (R1) to the inverting terminal, with a feedback branch of Resistor (R2) in series with capacitance (C1) to the output V_output Voltage; non-inverting terminal grounded.
 
Attachments
  • Handwritten-style slide deriving the output of an integrating op-amp circuit using KCL: 0 = U1/R + C dU2/dt = Uin/R + C dUout/dt, ending with Uout = -(t/RC) Uin, beside a schematic with input resistor, feedback capacitor and op-amp.
    upload_2018-5-2_18-2-12.png
    10.7 KB · Views: 1,492
  • Hand-drawn op amp circuit: input voltage V_INPUT through Resistor (R1) to the inverting terminal, with a feedback branch of Resistor (R2) in series with capacitance (C1) to the output V_output Voltage; non-inverting terminal grounded.
    lwwx9-jpg.jpg
    14.5 KB · Views: 1,466
maven sharma said:
View attachment 225039

yeah i can do it when its standard integrating op amp circuit but when a resister ans capacitor is added(see below image) to the inverting terminal in feedback then i don't know how to form equation
View attachment 225040
Handwritten KCL equations: I(INPUT) = I(capacitance) + I(Resistor2); I1 = Ic + I2; U1/R = [-Uout x C d/dt] + [Uout/R2].

Am I right?
 
Attachments
  • Handwritten KCL equations: I(INPUT) = I(capacitance) + I(Resistor2); I1 = Ic + I2; U1/R = [-Uout x C d/dt] + [Uout/R2].
    upload_2018-5-2_18-24-36.jpeg
    23.9 KB · Views: 1,309

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