Analog Integrated Circuits (Jieh Tsorng Wu)

The value of a can be found readily by letting k and

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Unformatted text preview: = a1 f • For constant input level, the harmonic distortions are 1 · HD2|T =0 HD2 = 2 (1 + T ) HD3 = 1− 2a 2 f 2 a3 (1+T ) (1 + T )3 · HD3|T =0 • For constant output level, the harmonic distortions are 1 · HD2|T =0 HD2 = (1 + T ) Feedback HD3 = 12-3 1− 2 2a2 f a3(1+T ) (1 + T ) · HD3|T =0 Analog ICs; Jieh-Tsorng Wu Series-Shunt Feedback Configuration Basic Amplifier ii v zi a×v io zo vo vi f × vo Feedback Network T =a×f Feedback vo a = vi 1+T Zi = zi × (1 + T ) 12-4 Zo = zo 1+T Analog ICs; Jieh-Tsorng Wu Shunt-Shunt Feedback Configuration ii Basic Amplifier i vi zi a×i io zo vo f × vo Feedback Network T =a×f Feedback vo a = ii 1+T zi Zi = 1+T 12-5 Zo = zo 1+T Analog ICs; Jieh-Tsorng Wu Shunt-Series Feedback Configuration ii vi i Basic Amplifier zi a×i io zo vo f × io Feedback Network T =a×f Feedback io a = ii 1+T zi Zi = 1+T 12-6 Zo = zo × (1 + T ) Analog ICs; Jieh-Tsorng Wu Series-Series Feedback Configuration Basic Amplifier ii v a×i zi io zo vo vi f × io Feedback Network T =a×f Feedback io a = vi 1 + T Zi = zi × (1 + T ) 12-7 Zo = zo × (1 + T ) Analog ICs; Jieh-Tsorng Wu Two-Port Analysis of Feedback Amplifier Topology Series-Shunt Series-Series Shunt-Series Sf b V V I So V I I For Li set vo = 0 io = 0 io = 0 For Lo set ii = 0 ii = 0 vi = 0 Source Thevenin Thevenin Norton Sf b = Feedback signal; So = Sampled Signal Li = Input loop loading; Lo = Output loop loading Shunt-Shunt I V vo = 0 vi = 0 Norton Fundamental Assumptions: 1. The input signal is transmitted to the output through the amplifier a and not through the f feedback network. 2. The feedback signal is transmitted from the output to the input through the f block, and not through the amplifier. 3. The feedback factor f is independent of the load and the source impedances. Feedback 12-8 Analog ICs; Jieh-Tsorng Wu Two-Port Analysis of Feedback Amplifier 1. Identify the topology. 2. Draw the basic amplifier circuit without feedback using the loading approximation method. 3. Use a Thevenin’s source if Sf b is a voltage and a Norton’s source if Sf b is a current. 4. Indicate Sf b and So on the “open-loop” circuit. Evaluate f = Sf b/So. 5. Evaluate forward gain a = So/Si from the open-loop circuit. 6. Calculate closed-loop characteristics. Feedback 12-9 Analog ICs; Jieh-Tsorng Wu Loading Approximation Method To find the input network: 1. Set vo = 0 for shunt sampling; i.e., short the output node. 2. Set io = 0 for series sampling; i.e., open the output loop. To find the output network: 1. Set vi = 0 for shunt comparison; i.e., short the input node. 2. Set ii = 0 for series comparison; i.e., open the input loop. Feedback 12-10 Analog ICs; Jieh-Tsorng Wu Two-Port Analysis of a Shunt-Shunt Feedback Amplifier RF RS vi vo is Zi Zo a= vo is if b = 0 RL i = s vs RS RL v if b = − Ro RF RL ro + (RF RL) T = a × f ≈ av × f= if b 1 =− vo RF RS RS + RF vo a 1 = ≈ ≈ −RF is closed loop 1 + af f Feedback RF vo F = (RS RF ri )(−av ) RS RF ri RF vi ≈ = Zi RS = av is 1+T −av vi ri RF RS vs io ro vi ⇒ vo RF ≈− vs RS ro RF RL ro vo ≈ = Zo RL = io 1+T 1+T 12-11 Analog ICs; Jieh-Tsorng Wu Return Ratio RS vi RF vo vs RL Return Ratio = R ≡ − RF vi RS ro vr −av vi ri vo vt RL vr vo vi vr = · ·− vt vt vo vi = RL [RF + (RS ro + RL [RF + (RS ri )] · RS ri ri )] RF + (RS ri ) · av • The loop gain T = a · f in the two-port analysis is an approximation of R. Feedback 12-12 Analog ICs; Jieh-Tsorng Wu Closed-Loop Gain Using Return Ratio sin sic ksic sr soc sout Rest of Circuit si c B1 = sout d si c B1 = si n Feedback soc =0 −H B2 si n soc sout B2 = soc soc = ksi c si n =0 si c H=− soc 12-13 sr R≡− = kH soc si n =0 sout d= si n soc =0 Analog ICs; Jieh-Tsorng Wu Closed-Loop Gain Using Return Ratio We have sout B1kB2 g +d = +d = A= si n 1 + kH 1+R g + d (1 + R) = A= 1+R g R +d R 1+R g = B1kB2 d 1 R + = A∞ · +d · 1+R 1+R 1+R A∞ g = +d R • d is the transfer function from the input to the output with k = 0. • The value of A∞ can be found readily by letting k → ∞ and si c is virtually “0”. • Typically, A∞ is determined by a passive feedback network and is equal to 1/f from two-port analysis. Feedback 12-14 Analog ICs; Jieh-Tsorng Wu Closed-Loop Gain Using Return Ratio The A∞R term can be rewritten as A∞ · R = g dH + d · R = B1kB2 + d R = B1 + B2 R si c = si n Feedback sout sout ×k × soc =0 · k · B2 si n =0 12-15 Analog ICs; Jieh-Tsorng Wu Blackman’s Impedance Formula Port X ix sic vx ksic sr soc Rest of Circuit vx a1 = si c a3 a2 a4 ix soc soc = ksi c vx = a1 · ZX = ix Feedback k =0 = a1 a2 a3 R(port X shorted) = −k a4 − a1 R(port X open) = −ka4 1 − k a4 − ⇒ vx ZX (k = 0) = ix a2 a3 a1 1 − ka4 1 + R(port X shorted) = ZX (k = 0) · 1 + R(port X open) 12-16 Analog ICs; Jieh-Tsorng Wu A Transresistance Feedback Amplifier VCC RF RC RF ir vo vo vbe iin rπ iin R=− A∞ = si c si n Feedback vo ii n = sout =0 gm = ∞ vbe ii n vo =0 it ro RC · (ro RC ) ro RC ir = · rπ · gm it...
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