Mismatch (VSWR) losses

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The power reflected from a mismatched load represents a loss, and will have implications that range from negligible to profound, depending on the situation For example, one result might be a slight loss of signal strength at a distant point from an antenna A more serious problem can result in the destruction of the output device in a transmitter The latter problem so plagued early solid-state transmitters that designers opted to include shutdown circuitry to sense high VSWR, and turn down output power proportionally In microwave measurements, VSWR on the transmission lines (that interconnect devices under test, instruments, and signal sources) can cause erroneous readings and invalid measurements Determination of VSWR losses must take into account two VSWR situations Figure 3-9 shows a transmission line of impedance Zo interconnecting a load impedance ZL, and a source with an output impedance Zs There is a potential for impedance mismatch at both ends of the line In the case where one end of the line is matched (either Zs or ZL), the mismatch loss caused by SWR at the mismatched end is ML = 10 log 1 SWR 1 SWR + 1

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92 Transmission lines which from Eq 352 is ML = 10 log (1 2) [355]

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Example 3-8 A coaxial transmission line with a characteristic impedance of 50 is connected to the 50- output (Zo) of a signal generator, and also to a 20-W load impedance ZL Calculate the mismatch loss Solution: (a) First find the VSWR: VSWR = Zo/ZL = (50 )/(20 ) = 25:1 (b) Mismatch loss: ML = 10 log 1 = 10 log 1 = 10 log 1 SWR 1 SWR + 1 25 1 25 + 1 15 35

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= 10 log [1 (043)2] = 10 log [1 0185] = 10 log [0815] = ( 10) ( 0089) = 089 When both ends of the line are mismatched, a different equation is required: ML = 20 log [1 ( 1 2)] where 1 is the reflection coefficient at the source end of the line, (VSWR1 1)/(VSWR1 + 1) 2 is the reflection coefficient at the load end of the line, (VSWR2 1)/(VSWR2 + 1) Note that the solution to Eq 356 has two values: [1 + ( 1 2)] and [1 ( 1 2)] The equations reflect the mismatch loss solution for low-loss or lossless transmission lines This is a close approximation in some situations; however, it is insufficient when the line is lossy Although not very important at low frequencies, loss becomes higher at microwave frequencies Interference between incident and re[356]

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Transmission line responses 93 flected waves produces increased current at certain antinodes which increases ohmic losses and increased voltage at certain antinodes which increases dielectric losses It is the latter that increases with frequency Equation 357 relates reflection coefficient and line losses to determine total loss on a given line n2 2 Loss = 10 log n n 2 where Loss is the total line loss in decibels is the reflection coefficient n is the quantity 10(A/10) A is the total attenuation presented by the line, in decibels, when the line is properly matched (ZL = Zo) Example 3-9 A 50- transmission line is terminated in a 30- resistive impedance The line is rated at a loss of 3 dB/100 ft at 1 GHz Calculate (a) loss in 5 ft of line, (b) reflection coefficient, and (c) total loss in a 5-ft line mismatched per above Solution: (a) A = (b) = 3 dB 5 ft = 015 dB 100 ft ZL Zo ZL + Zo 50 30 50 + 30 [357]

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= 20/80 = 025 (c) n = 10(A/10) = 10(015/10) = 10(0015) = 104 n2 2 Loss = 10 log n n 2 = 10 log = 10 log = 10 log (104)2 (025)2 104 (104) (025)2 1082 0063 104 (104) (0063) 1019 104 0066

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