BMEN 3350.001 (S’19) Homework 1 - Solution HW 1 Solution

(a) [5 points] In the circuit above, R a = R c = 100 Ω. Find R b and Rd such that V out = Adm V b − V a , where, the difference-mode gain is Adm = 1, and the common mode gain is zero (i.e. CMRR is infinity). (b) [10 points] Assume that one of the resistors you’ve used to build the circuit is not precise. If the actual value of Rb is 1% higher than what you’ve calculated in part (a), what is the CMRR of the difference amplifier in dB? (the other three resistors do not have any errors). Solution: (a) Vout = 1 Vb − Va The condition for this is, Rb Rd = = 1 Ra RcSince Ra = Rc= 100Ω; Ra and Ra need to be 100 Ω each. (b) Ra = Rc= Rd = 100 Ω; and R b = 101Ω 100 ∗ 201 101 V 0 = V b . − . V a = 1.005 ∗ V b − 1.01 ∗ V a 100 ∗ 200 100A cm A cm Therefore, Adm + = 1.005 and Adm − = 1.005 , which can be solved for 2 2 Adm = 1.0075 and Acm = −0.005 1.0075 CMRR = 20 log10 = 46.0855 dB −0.005