Open Loop Gain (Aol)
CIRCUIT
Schematic: Op_Amp_aol.asc
Op Amp Symbol: Opamp_1.asy
Op Amp Shematic: Opamp_1.asc
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SPEC IT
Intro 
One often overlooked parameter is the Op Amp's Open Loop Gain. Why?
It doesn't show up directly in the Closed Loop Gain equation.
But, what impact does it have on the actual gain? How can you ensure your design will meet spec? 
Definition 
Aol = vo / (vo+  vo) 
Design Goal 
Closedloop Gain Kcl = 100 V/V 
Design Spec 
Gain Error Max = 0.1% of Reading 
DESIGN IT
 Circuit Design
 Kcl = R2/R1+1 = 100V/V
 Choose: R1=10k
 Calc: R2=990k
 Op Model Param
 Circuit Test
 Input: .param Vstep=0.1V
 Expected Output: Vo = Vstep*Kcl = 1V*100 = 10V
TEST IT
 Run a Transient simulation. (.TRAN)
 Plot v(vo) and measure the output level.

Calc the lower limit to meet spec
of 0.1% (0.001)
 Vo_lim_lo = 10V*(1  0.001) = 9.99V
 Did it meet spec?
 If Vo > 9.99V, then PASS,
else FAIL
 DESIGN ISSUE: The accuracy fails to meet spec!
SOLVE IT
 Incrementally increase Aol (by factors of 2).
 Rerun the SPICE sim.
 Whats the minimum Aol needed for Vo > 9.99V?
THEORY REFRESH
 The ideal closed loop gain is
 However, this is just an approximation to the actual gain!
 where
 A = Aol = vo/(v+  v) (open loop gain)
 B = vfb/vo = R1/(R1+R2) (feedback gain)
 Notice how A directly impacts the actual gain! However, as A gets larger (A>>1), the actual gain approaches 1/B and you get the equation Kcl = 1/B = (R2+R1)/R1 above.
 So what’s the error (as a ratio) between Kcl_actual and Kcl?
 In other words, the accuracy depends on the total gain going forward
(A) and backward (B) around the loop.
 So, what happened to our initial design?
 Aol = 10000 and B = R1/(R1+R2) = 1/100 = 0.01
 The total Loop gain is Aol*B = 10000*(0.01) = 100
 Now estimate Gain_err = 1/(Aol*B) = 0.01
 This accounts for the original design not meeting the 0.1%
(0.001) spec!
 Let's solve it
 What is Aol required for a Gain_Err = 0.1% (0.001) and B = 0.01?
 Solve Gain_err = 1/(Aol*B) for Aol.
 Then calc Aol = 1/(Gain_Err x B).
 Retest the circuit with the new Aol. Did your circuit meet spec?
Way to go! Select an op amp that meets or exceeds your required Aol.
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