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# Opamps Design
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# Basic Op-Amp Design
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Op-amp fundamentals: ideal model, negative feedback, and open-loop behavior
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Welcome! These slides introduce the op-amp abstraction you'll use in analog design, including the ideal model, the actual operation of negative feedback, and why open-loop operation saturates.
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---
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## Ideal Op-Amp: Model
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Open-loop gain: $v_{out} = A (v_+ - v_-)$
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Ideal assumptions:
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• $A \to \infty$
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• Input currents: $i_+ = i_- = 0$
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• Output can source/sink as needed (within rails)
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• Infinite input impedance, zero output impedance
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The “ideal” device is an amplifier with huge differential gain. In practice, $A$ is large but finite and bandwidth-limited. Keep these as design heuristics (“golden rules”).
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---
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## Ideal opamp
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/assets/ideal.png
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size: contain
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---
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## Golden Rules (with Negative Feedback)
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1) No input current: $i_+ = i_- = 0$
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2) With negative feedback in linear region: $v_+ \approx v_-$
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When negative feedback closes the loop and the output is not saturated, the amplifier forces the differential input toward zero.
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---
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## Open-Loop vs Closed-Loop
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Open-loop:
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• Tiny differential input → huge $v_{out}$
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• Output rails → saturation
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Closed-loop (with feedback):
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• Gain set by resistors/network
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• Stable, predictable behavior
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Open-loop op-amps act like comparators (saturate high/low). Design uses closed-loop topologies to set usable gain/bandwidth.
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---
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## Inverting Amplifier
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Topology:
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• Input $v_{in}$ → $R_{in}$ → (−) node
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• Feedback $R_f$ from $v_{out}$ to (−)
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• (+) tied to reference (usually ground)
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Result (ideal):
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$G = \dfrac{v_{out}}{v_{in}} = -\dfrac{R_f}{R_{in}}$
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Speaker notes:
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Kirchhoff at the inverting node: no current into op-amp, so $(v_{in}-v_-)/R_{in} + (v_{out}-v_-)/R_f = 0$.
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With negative feedback in linear region $v_- \approx v_+ = 0$, giving $v_{out} = -\dfrac{R_f}{R_{in}} v_{in}$.
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---
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## Non-Inverting Amplifier
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Topology:
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• (+) sees $v_{in}$
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• Divider from $v_{out}$: $R_f$ to output, $R_g$ to ground into (−)
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Result (ideal):
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$G = \dfrac{v_{out}}{v_{in}} = 1 + \dfrac{R_f}{R_g}$
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Speaker notes:
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Use $v_- \approx v_+ = v_{in}$. The divider forces $v_- = v_{out}\dfrac{R_g}{R_f+R_g}$. Solve for $v_{out}$.
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---
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## Voltage Follower (Buffer)
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Topology:
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• Non-inverting with $R_f \to \infty, R_g \to \infty$ (direct feedback)
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• (+) = input, (−) = output
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Ideal result:
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$G = 1 \quad\text{and}\quad Z_{in}\to\infty$
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Provides isolation: high input impedance, low output impedance.
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---
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## Summing (Inverting) Amplifier
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Multiple inputs $v_{1..n}$ via $R_{1..n}$ into (−); feedback $R_f$.
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Ideal result:
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$v_{out} = -R_f\left(\dfrac{v_1}{R_1}+\dfrac{v_2}{R_2}+\cdots+\dfrac{v_n}{R_n}\right)$
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Great for weighted sums and simple DACs.
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---
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## Negative Feedback Intuition
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• Senses output error and drives $v_+ - v_- \to 0$
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• Sets closed-loop gain via passive network
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• Improves linearity and reduces sensitivity to op-amp $A$
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Speaker notes:
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As long as the op-amp isn’t saturating and has sufficient phase margin, the loop stabilizes with $v_+ \approx v_-$.
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---
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## Open-Loop Behavior (Comparator-like)
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With no feedback:
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• $A$ is huge ⇒ sign of $(v_+ - v_-)$ decides the rail
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• Output saturates near $+V_{rail}$ or $-V_{rail}$
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• Not for linear amplification
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Use a proper comparator IC for clean switching; many op-amps are slow or have input structures unsuited to rail-to-rail comparison.
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---
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## Practical Limits (Reality Check)
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Non-idealities:
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• Finite $A(s)$, finite bandwidth (GBW)
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• Input bias currents & offsets
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• Slew rate limits
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• Output swing vs rails & load
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Design with datasheet limits; verify stability with phase margin and consider source/load impedance.
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---
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## Quick Design Examples
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Inverting: Target $G=-10$ ⇒ pick $R_{in}=10\,\text{k}\Omega$, $R_f=100\,\text{k}\Omega$
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Non-inverting: Target $G=11$ ⇒ $R_f/R_g=10$ ⇒ $R_f=100\,\text{k}\Omega, R_g=10\,\text{k}\Omega$
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Speaker notes:
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Choose E-series values; check input/output swing vs rails and bandwidth: $f_{-3\text{dB}}\approx \dfrac{\text{GBW}}{G}$.
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---
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## Where Each Topology Shines
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Inverting:
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• Precise gains, easy summing, virtual ground node
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Non-inverting:
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• High input impedance, sensor buffering
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Follower:
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• Isolation between stages
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Pick based on source impedance and required gain.
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---
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## Wrap-Up
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• Ideal rules simplify analysis
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• Negative feedback sets the gain and linear region
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• Open-loop op-amps saturate—use comparators for switching
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Thank you! Questions?
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