240ln08 - COMPONENT MISMATCH IN DIFFERENTIAL AMPLIFIERS...

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1 COMPONENT MISMATCH IN DIFFERENTIAL AMPLIFIERS LN #8 (Pages 231 – 246 in the text) I os 2 V os - + IDEAL BALANCED DIFFERENTIAL AMPLIFIER INPUT OFFSET VOLTAGE V os INPUT OFFSET CURRENT I os For an emitter coupled DA 2 1 2 1 2 1 ln s s c c T BE BE ID I I I I V V V V = = The definition of V os is value of V ID for zero output I c1 R 1 = I c2 R 2 1 2 2 1 c c c c R R I I = Then = ) ( ) ( ln 2 1 1 2 1 2 VCB Q VCB Q A A R R V V B B c c T os I s =(qn i 2 D n /Q B (V CB ))A Using perturbation and the approximation ln (1+x) x , we have + B B c c T os Q Q A A R R V V Note the dependence on temperature T Vos dT dVos = By definition the offset current is 0 2 1 2 1 = > −− > −− = od B B c c os V when I I I I I β MOS SOURCE COUPLED PAIR Ios 0 by definition 2 2 1 1 2 1 2 1 ) / ( ' 2 ) / ( ' 2 L W k I L W k I V V V V V D D t t GS GS id + = = for 0 2 2 1 1 = = D D D D od R I R I V
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2 From small signal expansions, ( ) ( ) + = L W L W R R V V V V L L T GS t os / / 2 which is equation (3.248 ) in the text book. ****You will need to use this equation several times to solve problems**** In terms of mismatch, there are 4 gains of importance for the diff amp 0 | = = ic v id od dm v v A 0 | = = id v ic oc cm v v A 0 | = = ic v id oc cm dm v v A Differential-mode-to-common-mode gain which is the change in the cm output signal to the dm input 0 | = = id v ic od dm cm v v A Common-mode-to-differential-mode gain which is the change in the dm output signal to the cm input Some important results for these quantities can be obtained under the assumption that the signals controlling the mismatch generators can be found by analyzing the half-circuits without mismatch. The results are : 0 0 0 | 12 1 | 4 | id ic id dm m od m m cm dm v ic m T oc m dm cm v m vid m T oc m cm v ic m T A gR v g R gR A v v A v A v −= = ≈−
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240ln08 - COMPONENT MISMATCH IN DIFFERENTIAL AMPLIFIERS...

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