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# AMPLIFIER CRIB SHEET

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ECE137B High Frequency Amplifier Crib Sheet Page 1 Basics Transistor small signal high frequency models C B R C Vbe C Hybrid pi model Cm Cbc Cp Cbe Cp depl Cp diff Cp diff gm t f Ro ft gm 2 p Cp Cm gm a re Ic VT Rp b 1 re Ro VA IC gmVbe E Ro E re C T model Makes common base analysis much easier Both these models are only approximate being good up to ft Additionally Rb b is often an important parasitic not discussed much in 137B C Veb C gmVeb B Simplification of Emitter Degeneration approximate only check notes for bounds on validity C p Cp re re RE g m gm re re RE a re RE C m Cm R R r R r b 1 r R RE p Common Emitter Stage C B Ii Vbe Ri C gmVbe C CL RLeq p e E e Vout Vgen Vout Vgen e MB E 1 st zero 1 a1s a2 s 2 a1 Ri Cp Cm 1 gm RLeq RLeq Cm CL a2 Ri RLeq Cm CL Cm Cp Cp CL t zero Cm gm ECE137B High Frequency Amplifier Crib Sheet Page 2 Emitter Follower Stage C E R B Ii Vout Vgen Vout Vgen Ri CL Vbe RLeq C gmVbe MB 1 st zero 1 a1s a2 s 2 given that Avmb re re RLeq a1 Cp Rp re RLeq Ri 1 Avmb Cm Ri transistor input resistance CL RLeq transistor output resistance a2 Ri transistor input resistance RLeq re Cm Cp Cm CL CL Cp t zero gm Cp General Solutions of Problems Nodal analysis Know how to do this 1 Write the nodal equations sum of the currents 0 at each circuit node and put the resulting equations in matrix form the Y s being various combinations of gm s 1 R s and sC s Y11 Y12 Y13 Y14 V1 Vin Iin Y Y Y Y V2 0 21 22 23 24 Y31 Y32 Y33 Y34 V3 0 Y Y 41 42 Y43 Y44 V4 Vout 0 2 Use Cramer s rule to solve Y11 Y12 Y13 Iin Y21 Y22 Y23 0 Y31 Y32 Y33 0 Y41 Y42 Y43 0 Vout Y11 Y12 Y13 Y14 Y21 Y22 Y23 Y24 Y31 Y32 Y33 Y34 Y41 Y42 Y43 Y44 3 This comes out as Vout c c s c2 s 2 L ks m 0 1 d0 d1s d2 s 2 L Iin which is divided through to get 4 Vout Vout m 1 b1s b2 s 2 L s Iin Iin mb 1 a1s a2 s 2 L and the poles and zeroes are found by factoring the numerator and denominator The separated pole approximation if applicable makes this factoring easy if present m is the number of zeros minus the

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