Reflection coefficients The magnitude of the reflection coefficient (signified by in Software

Generator Universal Product Code version A in Software Reflection coefficients The magnitude of the reflection coefficient (signified by

or ) of a circuit or transmission line is simply the ratio between the reflected wave and the forward wave of a signal, or: VREFL VFWD and VSWR VSWR 1 1

The reflection coefficient will always be some value between 0 and 1, since the reflected wave s amplitude will never be higher in amplitude than the

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height of the forward wave Most values of , however, will contain both magnitude and phase, instead of simply magnitude as above These reflection coefficients are an indicator of the quality of the match between one impedance and another, or VREFL/VFWD, with a perfect match equaling zero and the worst match equaling 1 They can be expressed in rectangular ( R jX) or polar ( P 0) forms Nevertheless, calculating just the magnitude ratio will allow the computation of the return loss and mismatch for any circuit Return loss: RL (in dB) Mismatch loss: ML (in dB) 10 log10 10 log10 (1

old Y parameters (another way to characterize a transistor) into the newer S parameters, even though this is rarely required today Y11 Y12 (1 (1 S22) (1 S11) (1 S11) S22) S12 S21 (S12 S21) (S12S21) 1 50 1 50 1 50 1 50

2S12 S11) (1 S22) 2S21 S22) S22) S11)

(1 (1 (1

S11) (1 S11) (1 S22) (1

(S12S21) S12 S21 (S12 S21)

Use full vector values of S (Z 0 ) in calculations (for example, S11 035 45 ) We will have many instances when we have to convert from rectangular (Z R jX) to polar (Z R ) notation, and back, when designing amplifiers The manual technique below good only for positive real numbers is one method However, a simple scientific calculator performs the job much faster and more accurately 1 To convert rectangular into polar form (R jX to Z a Z R2 X 2 b tan 1 X/R (Note: tan 1 arc tangent) 2 To convert polar into rectangular form (Z a R Z (COS ) b X Z (SIN ) ):

to R jX):

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There are also many times when we must convert a series resistance and reactance into a parallel resistance and reactance This is in order to make a certain impedance-matching problem easier to solve Below is another technique for doing this To convert from series to parallel, using the example of Figs 345 and 346 (fC 15 GHz): 1 Find the Q of the series circuit: Q 2 If Q 3 If Q 4 XP 5 CP 6 LP 10, use RP 10, use RP RP QP 1 2 fXP 2 fXP (Q2 Q RS (Note: Q QS QP)

To convert from parallel to series using Figs 345 and 346: 1 Find Q 2 RS 3 RS 4 XS 5 CS 6 LS RP XP 1) if Q

if Q 10 RP )

accomplished by selective mismatching at either its input or output port This is an important technique, since we do not always require all of the gain that can be supplied by a particular transistor Thus, a stage can be designed for a certain gain (or NF) by actually not matching the load to the source by some predetermined amount This technique is a powerful and legitimate one, but it is wise to attempt it only when we are using an unconditionally stable transistor However, if the extra parts can be afforded in the amplifier design, fixed attenuators can also be adopted for this purpose where noise figure is not a concern To carry out selective output mismatching of a transistor amplifier in order to lower its gain by mismatch losses, follow this procedure (Fig 348): 1 Choose gain desired (GDESIRED) for the amplifier 2 Calculate ML where ML GMAX (dB) GDESIRED (dB) mismatch loss, dB

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