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Playing w/ RLC circuits (Part I)
11th January 2014
Anil Kumar Pugalia

© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
Agenda
●

RLC Basics

●

RC Visualization

●

CR Oscilloscope

●

Function Generator

●

Frequency Filters

© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
Introduction

V

~

I

V=I*R

R

V

~

I

V=I*Z

© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved

Z
Impedance (Z) Fundamentals
ω = 2πf

R⇒R

L⇒ j ω L

1
−j
C⇒
=
jωC ωC

Goal: Observe these phase shifts
© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
Basic RC Circuit
C
V

~

I
R

j
V =I∗Z , Z=R−
ωC

j
−j ϕ
Z=R−
=A e
ωC

√ω
A=∣Z∣=

2

2

2

R C +1
ωC
1
tan(ϕ)=arg Z=
ωRC
V V jϕ V
I = = e = <ϕ>
Z A
A

© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
RC Continued

√ω
A=

2

2

2

R C +1
1
, tan (ϕ)=
,
ωC
ω RC
C

V

~

VC
I

R
VR

V
I = <ϕ>
A
V ∗R
V R =I∗R=
<ϕ>
A
V =V m∗sin (ω t )

R
V R =(V m∗ )∗sin (ω t+ϕ)
A
R
ωRC
=
=α
2
A √ (ω R C ) +1

© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
RC Conclusion
V =V m∗sin (ω t )
VC
V

~

I
VR

V R =(V m∗α)∗sin (ω t+ϕ)
α=

ωRC

√(ω R C ) +1
2

1
tan(ϕ)=
ωRC
© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
RC Predictions
ωRC

1 , R=220Ω
α=
, tan(ϕ)=
2
ωRC
√(ω R C ) +1
f (Hz)
C (μF)

1000
α

2000

Ф (deg)

α

Ф (deg)

100

1.00

0.4

1.00

0.2

10

1.00

4.1

1.00

2.1

1

0.81

35.9

0.94

19.9

0.1

0.14

82.1

0.27

74.5

0.01

0.01

89.2

0.03

88.4

© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
Oscilloscope
●

Build your own

●

Total Cost: ~₹20,000

●

Parts
–

Computer (~₹20,000)

–

OSS: xoscope (₹0)

–

Audio Cable (~₹200)

●

Net Additional Cost: ~₹200

●

Limitations
–

Only for audio range (100Hz-20kHz)

–

DC is filtered off – shows AC with 0 average
© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
RC Predictions
ωRC

1 , R=220Ω
α=
, tan(ϕ)=
2
ωRC
√(ω R C ) +1
f (Hz)
C (μF)

1000
α

2000

Ф (deg)

α

Ф (deg)

100

1.00

0.4

1.00

0.2

10

1.00

4.1

1.00

2.1

1

0.81

35.9

0.94

19.9

0.1

0.14

82.1

0.27

74.5

0.01

0.01

89.2

0.03

88.4

© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
Function Generator
●

Build your own

●

Electronics-way: Use electronic components
–
–

●

555, Opamp, ...
Good got higher frequencies

Programming way: Use micro-controller
–

Like AVR, ...

–

Excellent for low frequencies

© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
FG Programming
●

Requirements for the uC
–
–

Digital to Analog Convertor (DAC), Or

–
●

Programmable Timer/Counter
Pulse Width Modulator (PWM)

Concept of FG
–

Run a frequency-divider timer/counter

–

Every count, generate the function output

–

Repeat for the frequency
© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
Sine Wave Example
-0.00000

sin(360°)

sin(198°)

-0.30902

sin(342°)

sin(144°)

sin(216°)

-0.58779

sin(324°)

0.80902

sin(126°)

sin(234°)

-0.80902

sin(306°)

sin(72°)

0.95106

sin(108°)

sin(252°)

-0.95106

sin(288°)

sin(90°)

1.00000

sin(0°)

0.00000

sin(180°)

sin(18°)

0.30902

sin(162°)

sin(36°)

0.58779

sin(54°)

sin(270°) -1.00000

Add +1 to make all positive.
Multiply by 5 / 2 to scale between 0 & 5.
2.50000

sin(360°)

sin(198°)

1.72746

sin(342°)

sin(144°)

sin(216°)

1.03054

sin(324°)

4.52254

sin(126°)

sin(234°)

0.47746

sin(306°)

sin(72°)

4.87764

sin(108°)

sin(252°)

0.12236

sin(288°)

sin(90°)

5.00000

sin(270°)

0.00000

sin(0°)

2.50000

sin(180°)

sin(18°)

3.27254

sin(162°)

sin(36°)

3.96946

sin(54°)

© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
Sine Wave Example (Contd.)
2.50000

sin(360°)

sin(198°)

1.72746

sin(342°)

sin(144°)

sin(216°)

1.03054

sin(324°)

4.52254

sin(126°)

sin(234°)

0.47746

sin(306°)

sin(72°)

4.87764

sin(108°)

sin(252°)

0.12236

sin(288°)

sin(90°)

5.00000

sin(270°)

0.00000

sin(0°)

2.50000

sin(180°)

sin(18°)

3.27254

sin(162°)

sin(36°)

3.96946

sin(54°)

●

We have 20 points

●

For f = 1kHz => T = 1/1kHz = 1ms

●

20 points in 1ms = 1000us

●

1 point in 50us => Timer trigger every 50us
© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
Frequency Filters
V =V m∗sin (ω t )

HPF =>

V R =(V m∗α)∗sin (ω t +ϕ)

LPF => V C =(V m∗√ 1−α )∗sin (ω t+(ϕ− π ))
2
ωRC
α=
=cos(ϕ)
VC
2
√(ω R C ) +1
1
I
tan(ϕ)=
VR
ωRC
2

V

~

C=1μF, R=10Ω => f=16kHz
© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
Wrap Up
●

Function Generator

●

Hobbyist Oscilloscope

●

RLC Basics

●

RC Visualization

●

RC Filters
Email: anil@computerclub.in
© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
Any Queries

© 2014 Computer Club of India (http://computerclub.in). All Rights Reserved

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Playing with R L C Circuits

  • 1. Playing w/ RLC circuits (Part I) 11th January 2014 Anil Kumar Pugalia © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 2. Agenda ● RLC Basics ● RC Visualization ● CR Oscilloscope ● Function Generator ● Frequency Filters © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 3. Introduction V ~ I V=I*R R V ~ I V=I*Z © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved Z
  • 4. Impedance (Z) Fundamentals ω = 2πf R⇒R L⇒ j ω L 1 −j C⇒ = jωC ωC Goal: Observe these phase shifts © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 5. Basic RC Circuit C V ~ I R j V =I∗Z , Z=R− ωC j −j ϕ Z=R− =A e ωC √ω A=∣Z∣= 2 2 2 R C +1 ωC 1 tan(ϕ)=arg Z= ωRC V V jϕ V I = = e = <ϕ> Z A A © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 6. RC Continued √ω A= 2 2 2 R C +1 1 , tan (ϕ)= , ωC ω RC C V ~ VC I R VR V I = <ϕ> A V ∗R V R =I∗R= <ϕ> A V =V m∗sin (ω t ) R V R =(V m∗ )∗sin (ω t+ϕ) A R ωRC = =α 2 A √ (ω R C ) +1 © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 7. RC Conclusion V =V m∗sin (ω t ) VC V ~ I VR V R =(V m∗α)∗sin (ω t+ϕ) α= ωRC √(ω R C ) +1 2 1 tan(ϕ)= ωRC © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 8. RC Predictions ωRC 1 , R=220Ω α= , tan(ϕ)= 2 ωRC √(ω R C ) +1 f (Hz) C (μF) 1000 α 2000 Ф (deg) α Ф (deg) 100 1.00 0.4 1.00 0.2 10 1.00 4.1 1.00 2.1 1 0.81 35.9 0.94 19.9 0.1 0.14 82.1 0.27 74.5 0.01 0.01 89.2 0.03 88.4 © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 9. Oscilloscope ● Build your own ● Total Cost: ~₹20,000 ● Parts – Computer (~₹20,000) – OSS: xoscope (₹0) – Audio Cable (~₹200) ● Net Additional Cost: ~₹200 ● Limitations – Only for audio range (100Hz-20kHz) – DC is filtered off – shows AC with 0 average © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 10. RC Predictions ωRC 1 , R=220Ω α= , tan(ϕ)= 2 ωRC √(ω R C ) +1 f (Hz) C (μF) 1000 α 2000 Ф (deg) α Ф (deg) 100 1.00 0.4 1.00 0.2 10 1.00 4.1 1.00 2.1 1 0.81 35.9 0.94 19.9 0.1 0.14 82.1 0.27 74.5 0.01 0.01 89.2 0.03 88.4 © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 11. Function Generator ● Build your own ● Electronics-way: Use electronic components – – ● 555, Opamp, ... Good got higher frequencies Programming way: Use micro-controller – Like AVR, ... – Excellent for low frequencies © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 12. FG Programming ● Requirements for the uC – – Digital to Analog Convertor (DAC), Or – ● Programmable Timer/Counter Pulse Width Modulator (PWM) Concept of FG – Run a frequency-divider timer/counter – Every count, generate the function output – Repeat for the frequency © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 13. Sine Wave Example -0.00000 sin(360°) sin(198°) -0.30902 sin(342°) sin(144°) sin(216°) -0.58779 sin(324°) 0.80902 sin(126°) sin(234°) -0.80902 sin(306°) sin(72°) 0.95106 sin(108°) sin(252°) -0.95106 sin(288°) sin(90°) 1.00000 sin(0°) 0.00000 sin(180°) sin(18°) 0.30902 sin(162°) sin(36°) 0.58779 sin(54°) sin(270°) -1.00000 Add +1 to make all positive. Multiply by 5 / 2 to scale between 0 & 5. 2.50000 sin(360°) sin(198°) 1.72746 sin(342°) sin(144°) sin(216°) 1.03054 sin(324°) 4.52254 sin(126°) sin(234°) 0.47746 sin(306°) sin(72°) 4.87764 sin(108°) sin(252°) 0.12236 sin(288°) sin(90°) 5.00000 sin(270°) 0.00000 sin(0°) 2.50000 sin(180°) sin(18°) 3.27254 sin(162°) sin(36°) 3.96946 sin(54°) © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 14. Sine Wave Example (Contd.) 2.50000 sin(360°) sin(198°) 1.72746 sin(342°) sin(144°) sin(216°) 1.03054 sin(324°) 4.52254 sin(126°) sin(234°) 0.47746 sin(306°) sin(72°) 4.87764 sin(108°) sin(252°) 0.12236 sin(288°) sin(90°) 5.00000 sin(270°) 0.00000 sin(0°) 2.50000 sin(180°) sin(18°) 3.27254 sin(162°) sin(36°) 3.96946 sin(54°) ● We have 20 points ● For f = 1kHz => T = 1/1kHz = 1ms ● 20 points in 1ms = 1000us ● 1 point in 50us => Timer trigger every 50us © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 15. Frequency Filters V =V m∗sin (ω t ) HPF => V R =(V m∗α)∗sin (ω t +ϕ) LPF => V C =(V m∗√ 1−α )∗sin (ω t+(ϕ− π )) 2 ωRC α= =cos(ϕ) VC 2 √(ω R C ) +1 1 I tan(ϕ)= VR ωRC 2 V ~ C=1μF, R=10Ω => f=16kHz © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 16. Wrap Up ● Function Generator ● Hobbyist Oscilloscope ● RLC Basics ● RC Visualization ● RC Filters Email: anil@computerclub.in © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved
  • 17. Any Queries © 2014 Computer Club of India (http://computerclub.in). All Rights Reserved