RF Amplifier Design. RF Electronics Spring, 2018 Robert R. Krchnavek Rowan University

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Jocelin Lambert
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1 RF Amplifier Design RF Electronics Spring, 2018 Robert R. Krchnavek Rowan University

2 Objectives Be able to bias an RF amplifier Understand the meaning of various parameters used to describe RF amplifiers Understand the derivation of various amplifier gains and be able to use them to design an appropriate RF amplifier. Be able to determine stability regions for an RF amplifier.

3 Generic Transistor Amplifier I C I B1 V CE

4 Amplifier Classes

5 See calculation on P Amplifier Efficiency

6 BJT Biasing Networks

7 BJT Biasing Networks

8 BJT Biasing Networks

9 FET Biasing Networks A MESFET usually requires: V G < 0 and V D > 0.

10 FET Biasing Networks Biasing the S-terminal can eliminate the need for a supply <0.

11 RF Amplifiers Gain and gain flatness (in db) Operating frequency and bandwidth (in Hz) Output power (in dbm) Power supply requirements (in V and A) Input and output reflection coefficients (VSWR) Noise figure (in db)

12 RF Amplifiers - Power Relations Combining the matching networks into the source and load: Further simplifying: Z S Z 0 Z L V S

13 RF Amplifiers - Power Relations What is the input power to the amplifier? V in = V + + V = V + (1 + Γ in )=V S Z in Z in + Z S Γ in = Z in Z 0 Z in + Z 0 =Γ 0 exp ( ȷ2βl) Z in = Z 0 1+Γ in 1 Γ in Γ S = Z S Z 0 Z S + Z 0 Z S = Z 0 1+Γ S 1 Γ S

14 RF Amplifiers - Power Relations V + = V S 1 Γ S 2(1 Γ in Γ S ) P in = 1 2 R (V ini in) P in = P + + P = 1 2 R [ (V + + V )( I + + I ) ] P in = P + + P = 1 2 R { [V + (1 + Γ in ) ] ( V + Z 0 V Z 0 ) } P in = P + + P = 1 8 V S 2 Z 0 1 Γ S 2 1 Γ in Γ S 2 ( 1 Γin 2)

15 RF Amplifiers - Power Relations An approach based on normalized power flow. V S Z S a S a 1 Γ S b 1 Z 0 Z L a 1 = a S +Γ S b 1 b 1 = a 1 Γ in a 1 = a S + a 1 Γ in Γ S a 1 = a S 1 Γ in Γ S

16 RF Amplifiers - Power Relations P in = P inc ( 1 Γin 2) = a 1 2 P in = P inc ( 1 Γin 2) = 2 a S = 1 Z0 V S Z 0 Z 0 + Z S = ( 1 Γin 2) a S 1 Γ in Γ S 2 2 Z0 Z 0 + Z S V S ( 1 Γin 2) P in = 1 2 Z0 Z 0 +Z S V S 2 1 Γ in Γ S 2 ( 1 Γin 2)

17 RF Amplifiers - Power Relations Do the two approaches (voltage vs normalized power) yield the same result? P in = 1 8 V S 2 Z 0 1 Γ S 2 1 Γ in Γ S 2 ( 1 Γin 2) versus P in = 1 2 Z0 Z 0 +Z S V S 2 1 Γ in Γ S 2 ( 1 Γin 2)

18 RF Amplifiers - Power Relations Available Power - P A The available power, P A, is the input power under conditions of maximum transfer of power (Γ in = Γ S *). For the voltage analysis: P A = P in Γin =Γ S = 1 8 V S 2 Z 0 1 Γ S 2 1 Γ in 2 2 ( 1 Γin 2) = 1 8 V S 2 Z 0 1 Γ S 2 1 Γ in 2 = 1 8 V S 2 1 Γ S 2 Z 0 1 Γ S 2 Similarly, for the normalized power analysis: P A = P in Γin =Γ S = 1 2 Z0 Z 0 +Z S V S 2 ( 1 Γin 1 Γ in 2 2 2) = 1 2 Z0 Z 0 +Z S V S 2 1 Γ in 2 = 1 2 Z0 Z 0 +Z S V S 2 1 Γ S 2 Note: The maximum available power is a function of Γ S.

19 RF Amplifiers - Power Relations G T = Transducer Power Gain - G T power delivered to the load available power from the source = P L P A Z S Z 0 Z L V S

20 RF Amplifiers - Power Relations Transducer Power Gain - G T P L = 1 2 V + L 2 Z 0 ( 1 ΓL 2) where V L + is the incident voltage at the load. The derivation of this expression is identical to the input power expression. through reflected at the load What is V + L? the amp and at the amp output V + S 21 + V + L Γ LΓ out = V + L V + L = V + S 21 1 Γ L Γ out = V + S 21 1 Γ L S 22

21 and, from previously RF Amplifiers - Power Relations Transducer Power Gain - G T V + 1 Γ S = V S 2(1 Γ in Γ S ) V + L = V S 1 Γ S 2(1 Γ in Γ S ) S 21 1 Γ L S 22 and so on...

22 RF Amplifiers - Power Relations Transducer Power Gain - G T a S Using normalized power flow: P A = 1 2 a S 2 1 Γ S 2 Z S V S a b 1 2 Γ Γ in Γ S out Γ b [S] L 1 b 1 ' a 2 b 1 " Z L P L = 1 2 b 2 2 ( 1 Γ L 2) a 1 = a S + b 1 Γ S b 1 = a 1 S 11 a S = a 1 b 1 Γ S b 1 = a 2 S 12 b 1 = b 1 + b 1 a S = a 1 Γ S (a 1 S 11 + a 2 S 12 )

23 RF Amplifiers - Power Relations Transducer Power Gain - G T a 2 = b 2 Γ L b 2 = a 1 S 21 + a 2 S 22 b 2 = a 1 S 21 + b 2 Γ L S 22 b 2 = a 1S 21 1 Γ L S 22 Z S a S a 1 b 2 a 2 = a 1S 21 Γ L 1 Γ L S 22 V S Γ Γ in Γ S out Γ b [S] L 1 b 1 ' a 2 b 1 " Z L

24 RF Amplifiers - Power Relations Transducer Power Gain - G T a S = a 1 Γ S (a 1 S 11 + a 2 S 12 ) a S = a 1 Γ S ( a S = a 1 [ 1 Γ S ( a 1 S 11 + a ) 1S 21 Γ L S 12 1 Γ L S 22 S 11 + S 21S 12 Γ L 1 Γ L S 22 )]

25 G T = RF Amplifiers - Power Relations Transducer Power Gain - G T G T = P L P A = b 2 2 a S 2 ( 1 ΓL 2)( 1 Γ S 2) a 1 S Γ L S 22 [ )] a 1 1 Γ S (S 11 + S 21S 12 Γ L 2 1 Γ L S 22 ( 1 ΓL 2)( 1 Γ S 2) ( 1 ΓL 2) S 21 2 ( 1 Γ S 2) G T = (1 S 11 Γ S )(1 S 22 Γ L ) S 21 S 12 Γ L Γ S 2

26 RF Amplifiers - Power Relations Defining Reflection Coefficients - Γ in, Γ out Γ in = b 1 = b 1 + b 1 a 1S 11 + S 12 = a 1 a 1 a 1 a 1 S 21 Γ L 1 Γ L S 22 Γ in = S 11 + S 21S 12 Γ L 1 S 22 Γ L Similarly, Γ out = S 22 + S 12S 21 Γ S 1 S 11 Γ S

27 RF Amplifiers - Power Relations Transducer Power Gain - G T Two additional forms of G T using the previously defined reflection coefficients: ( 1 ΓL 2) S 21 2 ( 1 Γ S 2) G T = 1 Γ S Γ in 2 1 S 22 Γ L 2 ( 1 ΓL 2) S 21 2 ( 1 Γ S 2) G T = 1 Γ L Γ out 2 1 S 11 Γ S 2

28 RF Amplifiers - Power Relations Unilateral Power Gain - G TU The unilateral power gain, G TU, assumes S 12 = 0. ( 1 ΓL 2) S 21 2 ( 1 Γ S 2) G TU = (1 S 11 Γ S )(1 S 22 Γ L ) 2 The unilateral power gain is often used to approximate the transducer power gain. It simplifies the design work.

29 RF Amplifiers - Power Relations Available Power Gain - G A The available power gain, G A, is the transducer power gain under conditions of load side matching (Γ out = Γ L *). G A = G T Γout =Γ L = power available from the amplifier power available from the source G A = S 21 2 ( 1 Γ S 2) ( 1 Γ out 2) 1 S 11 Γ S 2

30 RF Amplifiers - Power Relations Operating Power Gain - G The power gain, or operating power gain, G, is the ratio of the power delivered to the load to the power supplied to the amplifier. G = power delivered to the load power supplied to the amplifier G = P L P in = P L P A P A P in = G T P A G = ( 1 ΓL 2) S 21 2 P in ( 1 Γ in 2) 1 S 22 Γ L 2

31 Stability To maintain stability, we must eliminate positive feedback. We can guarantee stability by requiring the magnitude of the reflection coefficients be less than 1. Γ L < 1 Γ S < 1 S Γ in = 11 Γ L 1 S 22 Γ < 1 L S Γ out = 22 Γ S 1 S 11 Γ < 1 S where =S 11 S 22 S 12 S 21

32 Γ in = Stability Circles Note: At a given frequency, the S parameters are fixed. Therefore, to maintain stability in a design, only the reflection coefficients, and can be varied. L S S 11 Γ L 1 S 22 Γ < 1 L The reflection coefficient on the output,, affects. in L S 11 = S R 11 + ȷS11 I S 22 = S R 22 + ȷS I 22 = R + ȷ I Γ L =Γ R L + ȷΓ I L

33 Stability Circles

34 Stability Circles

35 Unconditional Stability

36 Design for Constant Gain Unilateral Design (S 12 0) G TU = 1 Γ S 2 1 S 11 Γ S 2 S Γ L 2 1 S 22 Γ L 2 = G S G 0 G L

37 Design for Low Noise

38 Design for Constant VSWR

39 Broadband, High-Power, and Multistage Amplifiers

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