Microwave Amplifiers I - Microwave Amplifiers Single Stage...

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1 Microwave Amplifiers - Single Stage Design [1] INTRODUCTION We limit this tutorial to single stage transistor amplifiers. Background material covering characteristics of microwave transistors and gain and stability of general two port amplifier circuits can be found in Chapter 11 of [1]. The relevant equations from those sections are reproduced here for completeness. Two-Port Power Gains The three types of power gains for an arbitrary two-port network connected to source and load impedances, Z S and Z L are: Power Gain = G = P L /P in is the ratio of power dissipated in the load Z L to the power delivered to the input of the two-port network. This gain is independent of Z S , although some active circuits are strongly dependent on Z S . Available Gain = G A = P avn /P avs is the ratio of the power available from the two-port network to the power available from the source. This assumes conjugate matching of both the source and the load, and depends on Z S but not Z L . Transducer Power Gain = G T = P L /P avs is the ratio of the power available from the two-port network to the power available from the source. This depends on both Z S and Z L . These definitions differ primarily in the way the source and load are matched to the two-port device; if the input and output are both conjugately matched to the two-port, then the gain is maximized and G = G A = G T . Equations for these gains in terms of the S parameters of the active device and the four different reflection coefficients, shown in Figure 1 and defined below, follow: Figure 1. A Two-port network with general source and load impedances. ( ) ( ) ( ) () 2 22 2 2 2 2 21 2 2 11 2 2 21 2 22 2 2 2 21 1 1 1 1 ) 3 ( 1 1 1 ) 2 ( 1 1 1 ) 1 ( L in S L S in L T out S S avs avn A L in L in L S S P P G S S P P G S S P P G Γ Γ Γ Γ Γ = = Γ Γ Γ = = Γ Γ Γ = = where 0 0 0 0 , ) 4 ( Z Z Z Z Z Z Z Z S S S L L L + = Γ + = Γ and
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2 S S out out out L L in in in S S S S Z Z Z Z b S S S S Z Z Z Z a Γ Γ + = + = Γ Γ Γ + = + = Γ 11 21 12 22 0 0 22 21 12 11 0 0 1 ) 5 ( 1 ) 5 ( Special cases of the transducer power gain occur when both the input and output are matched for zero reflection ( Γ L = S = 0) and when the device is unilateral ( S 12 = 0 or is negligibly small) so that in = S 11 . For these cases we have: ( ) ( ) 2 22 2 11 2 2 2 21 2 21 1 1 1 1 ) 7 ( ) 6 ( L S L S TU T S S S G S G Γ Γ Γ Γ = = Matching networks can be designed for various criteria such as maximum gain, specified gain or specified noise figure so that the circuit of Figure 2 can model the single-stage amplifier. Figure 2. The general transistor amplifier circuit. If we look at the transducer power gain of (3), we see that it accounts for both source and load mismatch. From (3), we can define separate effective gain factors for the input matching network, the transistor itself, and the output- matching network as follows: ( ) ( ) 2 22 2 2 21 0 2 2 1 1 ) 8 ( ) 8 ( 1 1 ) 8 ( L L L in S S S S G c S G b G a Γ Γ = = Γ Γ Γ = Then the overall transducer gain is G T = G S G 0 G L . If the transistor is unilateral, so that S 12 = 0 or is small enough to be ignored, then Γ
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This note was uploaded on 10/21/2011 for the course EE 4101 taught by Professor Yeotatsoon during the Spring '11 term at National University of Singapore.

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Microwave Amplifiers I - Microwave Amplifiers Single Stage...

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