Unity Gain Frequency (fu)
CIRCUIT
Schematic: Op_Amp_fu.asc
Op Amp Symbol: Opamp_1.asy
Op Amp Shematic: Opamp_1.asc
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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 MHz tr_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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