Highpass RC circuit

Linear Wave Shaping : RC HIghpass Circuit

1. Linear Wave shaping : RC High-Pass circuit Electronic Devices and Circuits UNIT – I SVEC19

2. The High-Pass RC Circuit When f= 0; X C = ∞ (Capacitor is open circuited); V o (t) = 0 ; then gain A= . When f increases , X C decreases , then output and gain increases. When f= ∞; X C = (Capacitor is short circuited); V o (t ) = V i (t) ; then gain A .   M.Balaji, Department of ECE, SVEC 2 The circuit which transmits only high- frequency signals and attenuates or stops low frequency signals.

3. Sinusoidal input M.Balaji, Department of ECE, SVEC 3 Laplace transformed High- P ass RC circuit frequency response

4. Putting s= j ,   M.Balaji , Department of ECE, SVEC 4

5. M.Balaji, Department of ECE, SVEC 5 Squaring on both sides and equating the denominators ,  

6. Step Voltage input A step signal is one which maintains the value zero for all times t < 0 ; and maintains the value V for all times t > 0 . M.Balaji, Department of ECE, SVEC 6 t = 0 - t = 0 + t < 0 t > 0 t = 0 The transition between the two voltage levels takes place at t = 0. V i = 0 , immediately before t = 0 (to be referred to as time t= 0 - ) and V i = V , immediately after t= 0 (to be referred to as time t= 0 + ).

7. Step input M.Balaji, Department of ECE, SVEC 7 Step input Step response for different time constants   V   When V f = 0

8. Pulse input The pulse is equivalent to a positive step followed by a delayed negative step. M.Balaji, Department of ECE, SVEC 8 Pulse waveform Pulse w aveform in terms of step

9. M.Balaji, Department of ECE, SVEC 9 RC >> t p

10. M.Balaji, Department of ECE, SVEC 10 RC comparable to t p

11. M.Balaji, Department of ECE, SVEC 11 RC << t p

12. M.Balaji, Department of ECE, SVEC 12 (a) RC >> t p (b) RC comparable to t p (c) RC << t p

13. Square wave input A square wave is a periodic waveform which maintains itself at one constant level V’ with respect to ground for a time T 1 , and then changes abruptly to another level V’’, and remains constant at that level for a time T 2 , and repeats itself at regular intervals of time T 1 +T 2 . A square wave may be treated as a series of positive and negative pulses. M.Balaji, Department of ECE, SVEC 13

14. M.Balaji , Department of ECE, SVEC 14 (a) Square wave input (b) When RC is arbitrarily large

15. M.Balaji, Department of ECE, SVEC 15 (c) RC > T

16. M.Balaji, Department of ECE, SVEC 16 (d) Output when RC comparable to T

17. M.Balaji, Department of ECE, SVEC 17 (e) Output when RC << T

18. Under steady state conditions, the capacitor charges and discharges to the same voltage levels in each cycle. So, the shape of the output waveform is fixed. the output is given by At t=T 1 ; the output is given by At t=T 1 +T 2 , Also   M.Balaji, Department of ECE, SVEC 18

19. Expression for the percentage tilt The expression for the percentage tilt can be derived when the time constant RC of the circuit is very large compared to the period of the input waveform, i.e RC >> T. For a symmetrical square wave with zero average value   M.Balaji, Department of ECE, SVEC 19

20. The output waveform for RC >> T is M.Balaji, Department of ECE, SVEC 20

21.     M.Balaji, Department of ECE, SVEC 21

22. When the time constant is very large, i.e , Where   M.Balaji, Department of ECE, SVEC 22

23. Ramp input M.Balaji, Department of ECE, SVEC 23 When a high- pass RC circuit is excited with a ramp input, i.e is the slope of the ramp then, From the Laplace transformed high-pass circuit, we get  

24. Taking inverse Laplace transform on both sides, we get For time t which are very small in comparison with RC, we have   M.Balaji, Department of ECE, SVEC 24

25. M.Balaji, Department of ECE, SVEC 25 The above figures shows the response of the high-pass circuit for a ramp input when (a) RC >> T and (b) RC << T, where T is the duration of the ramp. For small values of T, the output signal falls away slightly from the input.

26. High-Pass RC circuit as a differentiator Sometimes, a square wave may need to be converted into sharp positive and negative spikes (pulses of short duration). By eliminating the positive spikes, we can generate a train of negative spikes and vice-versa. The pulses so generated may be used to trigger a multivibrator . If in a circuit, the output is a differential of the input signal, then the circuit is called a differentiator. M.Balaji, Department of ECE, SVEC 26

27. then the circuit works as a differentiator 1/f ; here frequency must be small. At low frequencies, The voltage drop across R is very small when compared to the drop across C. ( ) Differentiating on both sides we get Thus , the output is proportional to the derivative of the input.   M.Balaji, Department of ECE, SVEC 27 V is small

28. Numerical Problem 1 A 1KHz symmetrical square wave of is applied to an RC circuit having 1ms time constant. Calculate and plot the output for the RC configuration as a High-Pass RC circuit. Solution: Given Peak-to –peak amplitude V PP = 10- (-10)=20V Since RC is comparable to T, the capacitor charges and discharges exponentially.   M.Balaji, Department of ECE, SVEC 28

29. High-Pass RC circuit M.Balaji, Department of ECE, SVEC 29

30. When the 1 KHz square wave shown by dotted line is applied to the RC high pass circuit. Under steady state conditions the output waveform will be as shown by the thick line. Since the input signal is a symmetrical square wave, we have   M.Balaji, Department of ECE, SVEC 30

31.   M.Balaji, Department of ECE, SVEC 31

32. Numerical Problem 2 If a square wave of 5 KHz is applied to an RC high-pass circuit and the resultant waveform measured on a CRO was tilted from 15V to 10V, find out the lower 3-dB frequency of the high-pass circuit. Sol: f= 5 KHz = 15V   M.Balaji, Department of ECE, SVEC 32

33. Peak-to-peak value of input Also% tilt   M.Balaji, Department of ECE, SVEC 33