2R-1C Combination Step Input Voltage Response | RC Circuit Analog Interview Questions

In my previous post RC Circuit Analysis , I have described the fundamentals of simple Analog RC circuit which is the backbone of all other RC circuit combination analysis. I highly recommend to go through the previous post RC Circuit Analysis to get familiarize with fundamentals of RC analysis.

In this post we are going discuss the behaviour of 2R-1C RC circuit excited with step voltage input. In our analysis all the components are considered ideal.

The 2R-1C combination RC circuit is given below.

2R_1C circuit step response

 

From our earlier analysis in RC Circuit Analysis , we are aware that we need to find out the voltage across capacitor and current flowing through it at time t=0+ and t=infinity.

Analysis at time t=0+

Now, for the above circuit, before application of  input voltage capacitors is fully discharged (voltage across it = 0 v). After application of step voltage, from  the fundamental property of capacitors, the capacitor will prevent the sudden change of the voltage across it and will try to remain at voltage=0. 

From our previous analysis, at t=0+ the circuit will look like below.

2r_1c_ckt_underStep_response

 

In the above circuit, we can see capacitor is behaving like a short circuit. This gives us the voltage across capacitor at t=0+ is zero. So, the current that flows through  the circuit is i(t=0+)=\frac{V1}{R1} . The voltage across resistor R1, V_R1, is same as input voltage V1.

Analysis at time t=infinity

From our previous post with 1R-1C circuit, we know that when capacitor is fully charged it acts like an open circuit and no current flows through it. Keeping this in mind, at t=infinity, let’s say capacitor C2 charges fully, behaves as an open circuit and current flowing through is zero.  The circuit becomes a series combination of two resistors and input voltage source at t=infinity.

2R_1C_ckt_2

From voltage divider rule, the voltage across capacitor C2 ( or resistor R2, both are in parallel)  can be written as below-

V_c_2=V_R_2=\frac{R2}{R1+R2}V1

The time constant of the circuit can be calculated by shorting the voltage source and calculating R_t_h and C_e_f_f.

Here, R_t_h=R1||R2,  C_e_f_f=C2,   time constant     \tau=C2*(R1||R2)

Below shows the simulation result in LTspice.

2R_1C_circuit_3

 

2R_1C_circuit_4

 

Feel free to comment if you have any questions/suggestions.

Check All the RC circuit related posts.

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