Non-Inverting Amplifier Gain Derivation with Finite Open Loop Gain Analysis

NON-INVERTING AMPLIFIER GAIN DERIVATION with FINITE OPEN LOOP GAIN ANALYSIS ASSUMPTIONS: INFINITE INPUT IMPEDANCE: ∴ i+ = 0; ZERO VOLTAGE DROP BETWEEN INPUTS, and A = ∞ . i− = 0 ZERO AC INPUT CURRENT. ASSUMPTIONS HOLD FOR A >> AV = 1 + Rs 3 +15 + 7 6 A + _ v+ vin 2 4 - Let Rs = 0; Therefore v+ = vin R1 v− = but v+ = v− × vout ; R 1+ R 2 + -15 v- R2 R1 vout R2 _ R1 so vin = R1 × vout ; R1 + R 2 vout R1 + R 2 = vin R1 or Av = 1 + vout R2 R1 FINITE OPEN-LOOP GAIN ANALYSIS: R1 R1 = Avid = A( v+ − v− ) = A( vin − v− ); v− = vout = βvout where β = . R1 + R2 R1 + R2 β is called the feedback transfer function and represents the fraction of the output voltage that is fed back from the output to the input. Combining the equations above gives: vout A vout = A[ vin − βvout ]; vout + Aβvout = Avin ; = Av = vin 1 + Aβ This gives the classic negative feedback amplifier gain expression. The product Aβ is called the loop gain or loop transmission. For Aβ>>1, Av approaches the ideal gain expression found above [=1/β]. In reality, A is a function whose value decreases with increasing frequency, until, at some point when Aβ is no longer >>1, the ideal gain equation, a function of only two resistor values, no longer Page 1of 1 3/3/03 Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. applies. Av drops at those high frequencies where the value of A approaches the value of Av. [Note: A = Avol] Page 1of 1 3/3/03 Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].