Describes the response of RC LPF to sinusoidal input

1. ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
ECE 216 Electronic circuits and Analysis-I
➢Academic year : 2020-21
➢Class & Section : 2/4 ECE-C
➢Name of the Faculty : Mr.D.Anil Prasad
ANIL PRASAD DADI/DEPT OF ECE/ANITS

2. ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
Linear Wave shaping circuits
Lecture #1
Frequency Response of RC
Low-pass Circuit for
Sinusoidal Input
ANIL PRASAD DADI/DEPT OF ECE/ANITS

3. Contents
1. Introduction
2. Frequency Response of RC Low-pass Circuit for Sinusoidal Input
3. Magnitude and phase response
4. Output voltage Equation
5. Summary
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
ANIL PRASAD DADI/DEPT OF ECE/ANITS

4. Introduction
➢ Altering the shape of the non-sinusoidal signal by transmitting it through a
linear network is called Linear Wave shaping.
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
ANIL PRASAD DADI/DEPT OF ECE/ANITS

5. Introduction
Outcome: Analyze the response of linear wave shaping circuits for the
given non sinusoidal input signals such as step, pulse, square wave
and ramp.
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
ANIL PRASAD DADI/DEPT OF ECE/ANITS

6. Introduction
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
R
C
+
-
Vi(t)
+
-
V0(t)
C
R
+
-
Vi(t)
+
-
V0(t)
RC Low Pass Filter RC High Pass FilterANIL PRASAD DADI/DEPT OF ECE/ANITS

7. Introduction
ANIL PRASAD DADI/DEPT OF ECE/ANITS
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
Vi(t) v0(t)
R
C
+
-
+
-
Vi(t) v0(t)R
C
+
-
+
-
RC Low Pass Filter RC High Pass Filter

8. Know about the capacitor
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
10V VC1
R=1KΩ
0.1μF
+
-
+
RC Low Pass Filter
-
10V VC3
R=1KΩ
10μF
+
-
+
RC Low Pass Filter
-
10V VC2
R=1KΩ
1μF
+
-
+
RC Low Pass Filter
-
Circuit 1 Circuit 3Circuit 2
VC1=? VC2=? VC3=?10V 10V10V
ANIL PRASAD DADI/DEPT OF ECE/ANITS

9. Know about capacitor
➢Capacitor starts charging when current enters into it.
➢It takes 5τ seconds to completely charge
➢It takes 5τ seconds to completely discharge
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
ANIL PRASAD DADI/DEPT OF ECE/ANITS

10. Know about the capacitor
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
10V VC1
R=1KΩ
0.1μF
+
-
+
RC Low Pass Filter
-
10V VC3
R=1KΩ
10μF
+
-
+
RC Low Pass Filter
-
10V VC2
R=1KΩ
1μF
+
-
+
RC Low Pass Filter
-
Circuit 1 Circuit 3Circuit 2
VC1=10V VC2=10V VC3=10V
Ʈ=0.1ms Ʈ=1ms Ʈ=10ms
ANIL PRASAD DADI/DEPT OF ECE/ANITS

11. Know about the capacitor
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
1V VC1
R=1KΩ
1μF
+
-
+
RC Low Pass Filter
-
100V VC3
R=1KΩ
1μF
+
-
+
RC Low Pass Filter
-
10V VC2
R=1KΩ
1μF
+
-
+
RC Low Pass Filter
-
Circuit 1 Circuit 3Circuit 2
VC1=? VC2=? VC3=?
Ʈ=1ms Ʈ=1ms Ʈ=1ms
1V 100V10V
ANIL PRASAD DADI/DEPT OF ECE/ANITS

12. Why LPF & HPF
ANIL PRASAD DADI/DEPT OF ECE/ANITS
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
Vi(t) v0(t)
R
C
+
-
+
-
Vi(t) v0(t)R
C
+
-
+
-
RC Low Pass Filter RC High Pass Filter
Xc=
1
ω𝑐
=
1
2π𝑓𝑐
C
0
f

13. Frequency response of RC LPF circuit for
sinusoidal input
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
Vi(t)=R i(t) +XC i(t)
Vi(t) v0(t)
R
C
+
-
+
-
➢At very large frequencies, XC=0 and
Capacitor becomes Short circuit
i(t)
i(t)=
𝑉𝑖
(𝑡)
𝑅
Vo(t)=XC i(t)=0
ANIL PRASAD DADI/DEPT OF ECE/ANITS

14. Frequency response of RC LPF circuit for
sinusoidal input
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
H(s)=
𝑉0
(𝑠)
𝑉𝑖
(𝑠)
Vi(t) v0(t)
R
C
+
-
+
-
i(t)
V0(t)=Vi(t)
𝑋 𝐶
𝑅+𝑋𝐶
V0(s)=Vi(s)
𝑋 𝐶
𝑅+𝑋𝐶
H(s)=
𝑋 𝐶
𝑅+𝑋𝐶
H(s)=
1
1+𝑆𝐶𝑅
H(f)=
1
1+𝑗2π𝑓𝐶𝑅 ANIL PRASAD DADI/DEPT OF ECE/ANITS

15. Frequency response of RC LPF circuit for
sinusoidal input
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
∠H(f)=∠θ= −𝑡𝑎𝑛−1 𝑓
𝑓 𝐻
Vi(t) v0(t)
R
C
+
-
+
-
i(t)
H(f)=
1
1+𝑗2π𝑓𝐶𝑅
H(f)=
1
1+𝑗
𝑓
𝑓 𝐻
fH=
1
2π𝑅𝐶
|H(f)|= 𝐴 =
1
1+
𝑓
𝑓 𝐻
2
𝐴 = 𝜋𝑟2
ANIL PRASAD DADI/DEPT OF ECE/ANITS

16. Frequency |A| |θ|
f=0 Hz 1 00
f<fH ≈1 00<θ<450
f=fH V0=0.707Vi 450
f>fH ≈0 450<θ<900
f=∞ 0 900
Frequency response of RC LPF circuit for
sinusoidal input
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
Vi(t) v0(t)
R
C
+
-
+
-
i(t)
𝐴 =
1
1 +
𝑓
𝑓 𝐻
2
𝐴 = 𝜋𝑟2
θ= −𝑡𝑎𝑛−1 𝑓
𝑓 𝐻
ANIL PRASAD DADI/DEPT OF ECE/ANITS

17. Frequency |A| |θ|
f=0 Hz 1 00
f<fH ≈1 00<θ<450
f=fH V0=0.707Vi 450
f>fH ≈0 450<θ<900
f=∞ 0 900
Frequency response of RC LPF circuit for
sinusoidal input
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
𝐴 =
1
1 +
𝑓
𝑓 𝐻
2
𝐴 = 𝜋𝑟2
θ= −𝑡𝑎𝑛−1 𝑓
𝑓 𝐻
fH f
Av(max)
0
0.707Av(max)
0
-450
-900
f
fH
Magnitude Response
Phase ResponseANIL PRASAD DADI/DEPT OF ECE/ANITS

18. Definition of Low Pass Filter
➢Low pass filter is a circuit which passes only low frequency signals and
attenuates high frequency signals when passed through a network over
certain cutoff frequency and it is determined by the RC time constant.
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
ANIL PRASAD DADI/DEPT OF ECE/ANITS

19. Definition of High Pass Filter
➢A high pass filter is a filter which passes high-frequency signals and
attenuates low-frequency signals when passed through a network over
certain cutoff frequency and it is determined by the RC time constant.
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
ANIL PRASAD DADI/DEPT OF ECE/ANITS

20. Output Voltage Equation
➢Vf=Output voltage at t=∞
➢Vi=output voltage at t=ti
➢ti= time at which input is applied
➢𝜏= time constant
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
V0(t)=Vf - (Vf-Vi)𝑒−
(𝑡−𝑡𝑖)
𝜏
ANIL PRASAD DADI/DEPT OF ECE/ANITS

21. Summary
1. RC Low Pass Filter
2. Frequency Response of RC Low-pass Circuit for Sinusoidal
Input
3. Magnitude and phase response
4. Output voltage Equation
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering
ANIL PRASAD DADI/DEPT OF ECE/ANITS

22. Thank you
For listening
ANIL PRASAD DADI/DEPT OF ECE/ANITS
ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES(A)
Department of Electronics and Communication Engineering