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	Closed-loop 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
  • Aol=10000 fu=1e6 Ro=1
• 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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