ECE 580 – Network Theory Transfer Function for Two-Port ...
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ECE 580 – Network Theory Transfer Function for Two-Port Networks Sec. 5 Temes-Lapatra 31 Transfer Function for Two-Port Networks Two-port networks are constrained to have the same currents at each port: I 1 ’ = I 1 , I 2 ’ = I 2 Hence, there are 4 unknowns: I 1 , V 1 , I 2 and V 2 . The source and load provide 2 relations between these, so the two-port must give 2 more for an analyzable linear circuit.
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Transcript of ECE 580 – Network Theory Transfer Function for Two-Port ...
ECE 580 – Network Theory Transfer Function for Two-Port Networks Sec. 5 Temes-Lapatra
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Transfer Function for Two-Port Networks Two-port networks are constrained to have the same currents at each port: I1’ = I1, I2’ = I2 Hence, there are 4 unknowns: I1, V1, I2 and V2. The source and load provide 2 relations between these, so the two-port must give 2 more for an analyzable linear circuit.
ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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Example:
€
V1 = AV2 − BI2I1 = CV2 −DI2
€
V2 = −R2R1V1 → A = −
R1R2, B = 0
€
I1 =V1R1
= AV2R1
= −V2R2
→ C = −1R2, D = 0
€
AD − BC = 0 − 0 ≠1
€
−R1R2
0
−1R2
0
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
⇒ non − reciprocal
ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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A transmission zero is a value of s (or frequency) for which the output signal equals zero even though the input was nonzero. Example: ladder network
Parallel branches across ports → yij simplest !
ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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How to find a new set of two-port parameters from a given one:
Example: Find the H parameters from the Z ones. We want
V1 = h11I1 + h12V2 I2 = h21I1 + h22V2
From second Z equation:
V2 = z21I1 + z22I2
€
I2 =Ih22
⎛
⎝ ⎜
⎞
⎠ ⎟ V2 −
z21h22
⎛
⎝ ⎜
⎞
⎠ ⎟ I1 ←
Plug I2 in first equation:
V1 = z11I1 + z12I2 = z11I1 +
€
z12z22
⎛
⎝ ⎜
⎞
⎠ ⎟ (V2 − z21.I1)
€
V1 =z12 /z22h12
V2 +z11 − z12z21 /z22
h11 ←
Comparing (A) and (B) with the H equations shows that h11 = det Z / z22, h12 = z12 / z22 ,
h21 =
€
− z21 z22 , and h22 =
€
1z22
See Table 1 on p. 166 in B&B for a complete set of formulas. In general, rewrite original
Equations:
V1 = z11I1 + z12I2 → V1-z12I2 = (z11I1) = a1 V2 = z21I1 + z22I2 → 0 + z22I2 = (v2 – z21I1) = a2
Solve for V1 and I2 in terms of I1, V2.
ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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Before added short, I1a = Iʹ′1a guaranteed; afterwards, if V=0, I also = 0, so I1a = Iʹ′1a still holds. Added short needed when finding y11 and y21.
For I1 = 1, I2 = 0, I3 = I1 = 1:
Z11 = V1 =Z1 + V1a + Z3 = Z11a + Z11b Z21 = V2 = V21 + Z3 = Z21a + Z21b
Same result for I2 = 1, I1 = 0.
ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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ECE 580 – Network Theory Two-Port Networks Chap 3 Balabanian-Bickart
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Just as in the case of two-ports, it is possible to interconnect multi-ports. Two multi-ports
are said to be connected in parallel if their ports are connected in parallel in pairs. It is not,
in face, necessary for the two multi-ports to have same number of ports. The ports are
connected in parallel in pairs until we run out of ports. It does not matter whether we run
out for both networks at the same time or earlier for one network. Similarly, two multi-
ports are said to be connected in series if their ports are connected in series of pairs.
Again, the two multi-ports need not have the same number of ports.
As in the case of two-ports, the overall y-matrix for two n-ports connected in
parallel equals the sum of the y-matrices of the individual n-ports. Similarly, the overall
z-matrix of two n-ports connected in a series equals the sum of the z-matrices of the
individual n-ports. This assumes, of course, that the interconnection does not alter the
parameters of the individual n-ports.
