Analog Circuit Analysis and Simulation By Using PSpice Introduction This experiment will expose you to a very valuable tool-PSpice. This will also develop skills in plotting curves, sketching functions and extracting parameters. You will use it quite often through all labs in PC203 and compare the experiment with the simulations. Theory Series Resonance From AC circuit theory, we know that the magnitude of the impedance of a series RLC circuit, as shown in Fig.1, is given by: 1 2 ) (1) Z = R 2 + (ωL − ωC Clearly, the impedance will be a minimum at a frequency 1 1 ( 2) f0 = 2π LC Figure 1 Series LRC Circuit The AC current in the circuit is clearly a maximum at the resonance frequency f0 , with a value of Z (f=f0 ) = Z0 , and will decrease for frequencies above and below the resonance frequency. The width of the resonance peak is an important quantity | it is related to the amount of energy dissipated by the resistance. We define a parameter, called the Quality Factor Q, which is the ratio of reactive power to average power and is given by: Q= ω0 ∆ω (3) is equal to Q= ω0 L R ( 4) If R is just RL then ω L (5) Q= 0 RL where RL – the internal resistance of the inductor L. It can also be shown that ω± are the frequencies at which the phase angle θ(Z)=±45o Parallel Resonance The situation described in the previous section is altered if the components are connected in parallel, as in Fig. 2. The impedance of this circuit is calculated by Eq.(6). This time, the circuit impedance is a maximum when the Figure 2: Parallel LRC Circuit frequency is equal to ω0. Clearly, the circuit current will be a minimum at this frequency. A plot of impedance vs. frequency will exhibit a peak centered at ω0, and the width of the peak determines the quality factor Q, as before. The frequencies ω+ and ω- , however, are the frequencies at which the impedance has decreased by a factor of 2 from its resonance value. 1 1 1 2 = ( ) 2 + (ωC − ) ( 6) Z R ωL Procedure Part A Stable Process when a Sinusoidal source is applied 1. Make a series and parallel RLC circuits as pictured as Fig.1 and Fig.2 by PSpice. To do following plotting you need to specify R=1K, L=0.6H and C=0.01µF for the two circuits. Also, you need to choose and specify VSIN or ISIN as a voltage source for the series or parallel RLC circuits. 2. Put a “Marker of Voltage or Current or Voltage Differential” inside the circuits. Open “Analysis Set Up” and then enable “AC Sweet” and specify it. 3. Plot V vs. f for series RLC and I vs. f for parallel RLC over a range of frequencies which is wide enough to show the asymptotic behavior of the function. Calculate f0 according to Eq.(2), and compare it with the curve you simulated. Change C from C=0.01µF to 0.1µF, and repeat again. Note that you need to use “decade” but not “Linear” in PSpice,. 4. Calculate Q just for series RLC circuit based on Eq.(3) and (4) respectively, and compare with your curve calculated by Eq.(3). 5. Simulate VR , VC and VL respectively for the series RLC circuit. Can you explain three curves varied with frequencies in such way? 6. Compare two circuits and discuss the interesting points as many as you can. Part B Transient Process when a square wave source is applied 1. As picture above, with R, C and VPULSE (you need to set all values for it) plot VR vs. t for a transient process by Pspice. Choose R=1k and C=0.01µF to 0.1µF. 2. Open “Analysis Set Up” and then enable “Transient” and specify it. 3. Change C from C=0.01µF to 0.1µF, and repeat again.