Two-Port Networks in Electrical Circuits
Explore the concept of two-port networks in electrical circuits, including analysis methods, parameters, and examples. Learn about the characteristics and superposition principle of two-port networks to enhance your understanding of circuit theory.
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Presentation Transcript
Lecture 27 Two-port Network Hung-yi Lee
Reference Chapter 14.1, 14.2, 14.3 (out of the scope)
Two and Three Terminal Networks i Circuit + Two- Terminal Network v Circuit Three-Terminal Network - i Chapter 2 Chapter 4.6
Four Terminal Network i1 = i3 i2 = i4 Input port Output port 4 parameters: i1, v2, i2, v2 (E.g. Filter)
Two-Port Network Is it a two-port network? i12 i2 i1 i11 i2 i1 Is it a two-port network?
Note Two-port network can be expressed by the phasor notation. A two-port network contains no independent sources, although it may contain controlled sources.
i-v characteristics Z parameters: = + V I I z z 1 11 z 1 I 12 z 2 I = + V 2 21 1 22 2 V I z 1 1 = V I 2 2 z z z 11 12 = z z 21 22
= + V I I z z 1 11 z 1 I 12 z 2 I Z parameters = + V 2 21 1 22 2 Superposition Principle: Any current (or voltage) for an element is the weighted sum of the voltage (or current) of the sources.
Z parameters How to find the Z parameters? = + V I I z z 1 11 z 1 I 12 z 2 I = + V 2 21 1 22 2 I1= 0 Set = = V I V I z z 12 1 2 22 2 2 I2= 0 Set = = V I V I z z 21 2 1 11 1 1
Z parameters Example 14.1 = + V I I z z 1 11 z 1 I 12 z 2 I = + V 2 21 1 22 2 I1= 0 Set R2 + R2 V sC R + = = = 1 V I z = I 12 1 2 2 2R 1 sC + R 2R 1 2 R 1 sC sC ( ) + + sCR2 R R 1 sC R ( ) = V I z = + = = || R 1 R sC 22 2 2 + + 2R 1 sC 2sCR 1
Z parameters Example 14.1 = + V I I z z 1 11 z 1 I 12 z 2 I = + V 2 21 1 22 2 I2= Find z11and z21 0 Set R2 sC z = = z 12 + 21 2 R 1 sC symmetric + sCR2 R = z z = 22 11 + 2sCR 1
Equivalent Two Port Network = + V I I z z 1 11 z 1 I 12 z 2 I = + V 2 21 1 22 2 Two Impedances, Two controlled sources Three Impedances, One controlled source
Equivalent Two Port Network Tee Network z z z 11 12 = z z 21 22 = = I1= V I z = = Z + V I z 0 c Z Z Set 22 2 2 12 1 2 b c = = = = Z + V I V I z z c Z Z I2= 0 Set 21 2 1 11 1 1 a c + Z Z Z Z z Reciprocal Network a c c = + Z Z c b c
Equivalent Two Port Network Tee Network = z + Z Z Z Z a c c + Z Z c b c Reciprocal Network z z z z z z z 22 11 11 z = z z 22
Equivalent Two Port Network = + = + V I I V I I z z z z 1 11 z 1 I 12 z 2 I 1 11 z 1 12 z 2 ( )1 I = + = + + V V I I z z 2 21 1 22 2 2 12 1 22 2 21 12 ( )1 I z z 21 12 z z z z 22 12 11 12 z 12
Other kinds of Parameters y parameters: Z parameters: I V V I y z 1 1 1 1 = = I V V I 2 2 2 2 = z y 1 The y parameters does not always exist. [z] is not always invertible.
4 2 C 6 kinds of Parameters z parameters: h parameters: T parameters: V I V I V V z h T 1 1 1 1 1 2 = = = V I I V I I 2 2 2 2 1 2 y parameters: g parameters: t parameters: I V I V V V g t y 1 1 2 1 1 1 = = = I V V I I I 2 2 2 2 2 1 Be careful!
T/t Parameters V V V V t T 2 1 1 2 = = I I I I 2 1 1 2 T/t for transmission 1I 2I For T For t Parameters Parameters
Connecting the Two-port Networks Parallel Connection: Series Connection: Cascade Connection:
Parallel Connection I I 2a 1a + + V I a y y 1 a 1 = V V 1 2 a V I 2 a 2 I I 2b 1b + + b y V I y V 1 b 1 = V 1 2 b V I 2 b 2
Parallel Connection I V I I y 1 a 1 = 2a 1a a V I 2 a 2 a y 1I 2I V I y 1 b 1 = + + b V I 2 b 2 V V I I 1 2 2b 1b I I I 1 1 1 a b = + V I I b y I 2 y 2 2 a b y 1 = + a b V 2 V I y y b y y 1 1 = + = par par a V I 2 2
Parallel Connection - Note Parallel two two-port network can break the port condition 5 + + V V 5 . 2 10 1 2 + + 10 V 5V + + 2 A 2 A 5 . 2 V V y y b y 2 1 = + 0 A 0 A par a 5 . 2
Series Connection 2I 1I + + a z V I z 1 1 a = V V 1a 2a a V I 2 2 a 2I 1I + + b z I V z 1 1 b = V V 1b 2b b I V 2 2 b
Series Connection V I z 1 1 a = a V I 2 2 a 2I 1I I V z 1 1 b = + + + + a z b I V 2 2 b V V 1a 2a V V V 1 1 1 a b = + 2I V 1I V 1 V V V 2 2 2 2 a b + + b z I z z V V 1 = + 1b 2b a b I 2 Not always true because parallel connection may also break the port condition z z b z = + ser a
Cascade connection V V V V T T 1 2 b = 2 1 a = b aI I I I 1 2 b 2 1 a V V V The overall T parameters equals the product of the individual T parameters. T a Tcas 1 2 = 2 = T b I I I 1 2 2
Cascade connection + V V V out in x 1 1 V V V V V sC sC out x out x out = = 1 2 1 1 V V V V V + + R R in x in in x 1 2 sC sC 1 2 V 1 out = ( ) + + + + 2 V 1 R R R s C C R C s C C R 1 1 2 2 1 2 1 2 1 2 in
V 1 out = ( ) + + + + 2 V 1 R R R s C C R C s C C R 1 1 2 2 1 2 1 2 1 2 in Cascade connection in I = I 0 out V V in out b T a T out V V A B A B V a T in = out = T b I I C D C ) ) V D 0 in out ( ( V V + A A C A B V A B V 1 out = out out = = + + C A C C D C D V A A B C out out in
Cascade connection 1I V V 2I V A B T 1 2 2 = = V = I I + + I C D 1 2 2 V V + V I A B 1 2 1 2 2 = + I V I C D 1 2 2 I V + R 1 sC sC I2= 0 1 1 = = = = = sC + C 1 1 sC A R1 1 1 1 V V 1 2 2 1 V2= 0 I V 1 1 D = B= = = R 1 1 I I 2 2
V 1 out = ( ) + + + + 2 V 1 R R R s C C R C s C C R 1 1 2 2 1 2 1 2 1 2 in Cascade connection in I = I 0 out V V in out b T a T + R sC 1 A B sC R Ta 1 1 1 = = V 1 C D 1 out 1 = + V A A B C + R sC 1 A B sC R Tb in 2 2 2 = = 1 C D 2
This Friday 2011 ( )
Acknowledgement (b02)
