Analog Interview Questions I

2. Find the voltages Vs, Vi and Vo in the circuit below

Solution:

Current I in the circuit is constant, so voltage across capacitor increases linearly with the slope I/C. voltage across resistor R is IR. So voltage Vi in the above circuit is Vi=IR + I/C*t.

Next question is very simple 

       3. A simple RC circuit is given with an impulse voltage signal at the input, plot the voltage across resistor and capacitor. Find the current waveform?

     Solution: 

      For ideal impulse voltage signal, voltage across capacitor is zero always. But voltage across resistor is same as impulse signal and current in the circuit is similar to ideal impulse I=Vin/R.. 

      But let us think about a practical impulse signal with finite pulse 'tw' and amplitude Vm. So the voltage across resistor and capacitor at t=0+ is Vm and 0. The voltage across capacitor increase with time constant RC during pulse 'tw', for time t>tw, impulse falls to zero so the capacitor will discharge to zero from the voltage it has charge earlier.Current I in the circuit is similar to VR except it is scaled by R i.e., I=VR/R

   
      4.  Given a simple RC circuit, find the voltage across resistor and capacitor for the ramp input with a slope k.    Find the current waveform in the circuit?
      Solution:
      Initially Vo=0V, so for a given ramp input since input is zero initially Vo will be zero. How should we analyse for inputs other than step? For any RC circuit, if current is finite, voltage across capacitor cannot change instantaneously. For ramp input initial current is zero since Vi is zero at t=0, so capacitor cannot charge so Vo is zero at t=0.
      Now as input increases, current tries to increase, so voltage across capacitor also increases but slowly since current is very small initially. Voltage across resistor is VR=IR. Current increases to a point when the slope of the output is equal to slope of the input, so that current is constant and is given by (Vo-Vi)/R.

       If you solve the differential equation for the RC circuit with ramp input you will get the above equations.
       In the figure below, current waveform is not given, since it is similar to voltage VR, except scaled by R i.e,         I=VR/R

       In the next post we will discuss RL circuit, which are similar to RC circuit, but lot of people get confused whenever they see inductor. We will find simple way of analyzing RL circuits. we will discuss important points about RC/RL circuits.

http://www.ee.ucr.edu/~rlake/EE135/Fuding_Ges_Guide.html
http://stevenic.blogspot.in/2010/04/some-on-site-interview-questions-fuding.html

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