Time and Frequency Responses of Rc, Rlc Circuits
Esc 102 Introduction to Electronics, 2004-2005/I
EXPERIMENT NO 4
TIME AND FREQUENCY RESPONSES OF RC, RLC CIRCUITS
Part A: Time Response of RC Circuits
Step response (or Time response) of RC and RL circuits is of great importance in the design of pulse circuits. The aim of this part of the experiment is to study the time response of RC circuits. In order to get time responses, Square-wave pulses of varying frequency are applied to the given RC circuits. The results obtained are then compared with theory.
1.1 RC Integrator Circuit
Wire the circuit of Fig.1. Connect the MAIN (FUNCTION) output of the Function Generator (FG) to the RC circuit and also to the CH-1 input of the CRO. Choose square wave signal. Adjust the amplitude control of the FG to obtain a waveform going from -5V to +5V. Connect the output of the RC circuit to CH-2 input of the CRO. Be sure to choose the "DC" mode for CH-1and CH-2 inputs so as to observe the dc levels of the signals.
(i) Time Response when T < τ : Choose the waveform frequency (f) to be 25KHz.
Observe and sketch Vi & Vo w.r.t. time. Note down the salient features of Vo.
(ii) Time Response when T = τ : Choose the waveform frequency (f) to be 5KHz.
Observe and sketch Vi & Vo w.r.t. time. Note down the salient features of Vo. Choose any two convenient points on the rising and falling part of Vo and measure the corresponding voltages and the time interval. From these readings obtain τ (=RC). Compare the results with the values used.
(iii) Step response when T > τ : Choose f= 500Hz. Observe and sketch Vi and Vo.
1.2 RC Differentiator Circuit
Wire the RC circuit of Fig.2. As in the case of RC integrator, obtain time response of RC circuit for the following three cases. Sketch Vi and Vo in each case.
(i) Step Response when T < τ (use f= 25 KHz).
(ii) Step Response when T = τ (use f= 5 KHz).
(iii) Step Response when T > τ (use f= 500 Hz).
(iv) Increase the input signal frequency beyond 40KHz and note the minimum frequency at which the linear tilt (droop) seen in the Vo waveform is negligible.
PART B: FREQUENCY RESPONSE OF RC & RLC CIRCUITS
RC and RLC circuits are often used in electronic circuits to achieve frequency selection. For example, RC and RLC filters are commonly used to pass a certain band of frequencies and to stop (or attenuate) another band of frequencies. For applications such as the above, it is important to know the frequency responses. The aim of this experiment is to study the frequency responses of some of the commonly used RC and RLC circuits. For this purpose sinusoidal signals of varying frequencies are applied to the input of these circuits and their output responses are observed and compared with theory.
2.1 RC Low Pass Circuit
Wire the RC Low pass circuit of Fig.3. Set up the FG to produce a sinewave of amplitude of 10V peak to peak (-5V to + 5 V). Connect Vi to CH-1 and Vo to CH-2 of the CRO. For several frequencies from about 40Hz to 40KHz, measure the peak-to-peak value of VO, keeping Vi= 5 sinwt (i.e. peak-to-peak = 10V). Calculate the gain, G(f)=|Vo/Vi |. (Take more readings around the -3dB point or cut off frequency). Plot the frequency response G(f) =20 log|Vo(f)/Vi(f)|, vs f on a semi-log graph paper. Measure the -3 dB frequency fc. Calculate ..fc = 1/2πRC, using the given R and C values. Compare this fc with the measured value.
2.2 RC High Pass Circuit
Wire the RC high pass circuit of Fig.4. Repeat steps of Sec.2.1.
2.3 RLC Bandpass Circuit
Wire the RLC circuit of Fig.5. Set up the FG to produce a sinewave of amplitude of 10V peak to peak (-5V to + 5 V). Connect Vi to CH-1 and Vo to CH-2 of the CRO. For several frequencies from about 40Hz to 100KHz, measure the peak-to-peak value of VO, keeping Vi= 5 sinwt (i.e. peak-to-peak = 10V). (Take more reading around the peak (fo) and the -3dB points, fL and fH). Calculate the gain, G(f)=|Vo/Vi |. Plot the frequency response G(f) =20 log|Vo(f)/Vi(f)|, vs f on a semi-log graph paper.
Measure the -3 dB frequencies fL and fH. Bandwidth of the RLC circuit is fH.- fL.
Calculate fo = 1/ (2p (LC) 1/2), using the given L and C values. Compare this fo with the measured value.
Quality factor (Q) of a bandpass filter is an index of the sharpness of the response. Q is generally required to be much greater than unity, as larger values of Q gives sharper frequency selection. Calculate Q of the above bandpass circuit from the measured values of fo, fH, and fL.,using the relation:
Q= fo/(fH – fL)
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