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# Unity Gain Frequency (fu)

## CIRCUIT

Schematic: Op_Amp_fu.asc
Op Amp Symbol: Opamp_1.asy
Op Amp Shematic: Opamp_1.asc
Right Click on filename, select "Save link as...",

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## SPEC IT

 Intro In sensor and signal acquisition systems, it's critical to respond to a voltage change quickly. A fast response requires a HIGH bandwidth (fc) and a SHORT settling time (tr). But beware, both an op amp's open-loop unity-gain freq (fu) and closed-loop signal gain (Kcl) can limit the circuit's overall bandwidth. A simple insight can ensure your design meets spec! Definition fu  - frequency where open-loop gain crosses unity.Aol(fu) = 1V/V (0dB) Design Goal Closed-loop Bandwidth:  fc = 1MHz Design Spec fc > 1.0 MHztr_63% < 0.159 us

## DESIGN IT

• Circuit Design
•  Kcl = (R2+R1)/R1 = 4V/V
• Choose: R1=10k
• Calc: R2=30k
• Op Model Param
• 1MHz device spec
• Aol=100000 fu=1e6 Ro=1
• Circuit Test
• Input: .param Vstep=2.5V
• Output:  Vo = Vstep*Kcl = 2.5V*4 = 10V
• Expected 63% Risetime: tr = 0.159us (fc = 1MHz)

## TEST IT

• Run a Transient simulation. (.TRAN)
• Plot v(vo) and measure the risetime (tr) to 63.7% or 6.37V
• Did it meet spec?
• If tr < 0.159us, then PASS, else FAIL
•  DESIGN ISSUE: The bandwidth fails to meet spec!

## SOLVE IT

• Incrementally increase fu (by factors of 2).
• Rerun the SPICE sim.
• What's the minimum fu needed for tr < 0.159us?

## THEORY REFRESH

• The closed-loop bandwidth (fc) is the unity-gain freq (fu) scaled by the feedback gain (B).

• where B is the gain from vo to vfb

• You can also think of fc as fu divided by Noise Gain Kn

• What is Kn? Simply the gain from the vin+ input to the output vo.

• Note these two handy insights for the non-inverting amp!
• The Noise gain equals Signal gain:
Kn = Kcl
• Noise Gain and Feedback gain are related by
Kn = 1/B
• What happened to our original design?
• B = R1/(R1+R2) = 0.25
• Kn = 1/B = (R1+R2)/R1 = 4
• fc = fu/Kn = 1MHz/4 = 250kHz.
• Yikes! The bandwidth is 4 times lower than the spec of 1MHz.
(Consequently, the rise time will be 4 times longer!)
• Let's solve it
• What fu is required for a fc = 1MHz and Kcl = Kn = 4?
• Solve fc = fu / Kn for fu.
• Then calculate fu = fc * Kn
• Retest the circuit with the new fu. Did your circuit meet spec?

Way to go! Select an op amp that meets or exceeds your required fu.

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