# Opamps Design
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# Basic Op-Amp Design
	Op-amp fundamentals: ideal model, negative feedback, and open-loop behavior

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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## Ideal Op-Amp: Model
	Open-loop gain: $v_{out} = A (v_+ - v_-)$
	Ideal assumptions:
	• $A \to \infty$
	• Input currents: $i_+ = i_- = 0$
	• Output can source/sink as needed (within rails)
	• Infinite input impedance, zero output impedance

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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## Ideal opamp
/assets/ideal.png
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## Golden Rules (with Negative Feedback)
	1) No input current: $i_+ = i_- = 0$
	2) With negative feedback in linear region: $v_+ \approx v_-$

When negative feedback closes the loop and the output is not saturated, the amplifier forces the differential input toward zero.

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## Open-Loop vs Closed-Loop
	Open-loop:
	• Tiny differential input → huge $v_{out}$
	• Output rails → saturation
	Closed-loop (with feedback):
	• Gain set by resistors/network
	• Stable, predictable behavior

Open-loop op-amps act like comparators (saturate high/low). Design uses closed-loop topologies to set usable gain/bandwidth.

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## Inverting Amplifier
	Topology:
	• Input $v_{in}$ → $R_{in}$ → (−) node
	• Feedback $R_f$ from $v_{out}$ to (−)
	• (+) tied to reference (usually ground)

	Result (ideal):
	$G = \dfrac{v_{out}}{v_{in}} = -\dfrac{R_f}{R_{in}}$

Speaker notes:
Kirchhoff at the inverting node: no current into op-amp, so $(v_{in}-v_-)/R_{in} + (v_{out}-v_-)/R_f = 0$.  
With negative feedback in linear region $v_- \approx v_+ = 0$, giving $v_{out} = -\dfrac{R_f}{R_{in}} v_{in}$.

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## Non-Inverting Amplifier
	Topology:
	• (+) sees $v_{in}$
	• Divider from $v_{out}$: $R_f$ to output, $R_g$ to ground into (−)

	Result (ideal):
	$G = \dfrac{v_{out}}{v_{in}} = 1 + \dfrac{R_f}{R_g}$

Speaker notes:
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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## Voltage Follower (Buffer)
	Topology:
	• Non-inverting with $R_f \to \infty, R_g \to \infty$ (direct feedback)
	• (+) = input, (−) = output

	Ideal result:
	$G = 1 \quad\text{and}\quad Z_{in}\to\infty$

Provides isolation: high input impedance, low output impedance.

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## Summing (Inverting) Amplifier
	Multiple inputs $v_{1..n}$ via $R_{1..n}$ into (−); feedback $R_f$.

	Ideal result:
	$v_{out} = -R_f\left(\dfrac{v_1}{R_1}+\dfrac{v_2}{R_2}+\cdots+\dfrac{v_n}{R_n}\right)$

Great for weighted sums and simple DACs.

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## Negative Feedback Intuition
	• Senses output error and drives $v_+ - v_- \to 0$
	• Sets closed-loop gain via passive network
	• Improves linearity and reduces sensitivity to op-amp $A$

Speaker notes:
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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## Open-Loop Behavior (Comparator-like)
	With no feedback:
	• $A$ is huge ⇒ sign of $(v_+ - v_-)$ decides the rail
	• Output saturates near $+V_{rail}$ or $-V_{rail}$
	• Not for linear amplification

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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## Practical Limits (Reality Check)
	Non-idealities:
	• Finite $A(s)$, finite bandwidth (GBW)
	• Input bias currents & offsets
	• Slew rate limits
	• Output swing vs rails & load

Design with datasheet limits; verify stability with phase margin and consider source/load impedance.

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## Quick Design Examples
	Inverting: Target $G=-10$ ⇒ pick $R_{in}=10\,\text{k}\Omega$, $R_f=100\,\text{k}\Omega$
	Non-inverting: Target $G=11$ ⇒ $R_f/R_g=10$ ⇒ $R_f=100\,\text{k}\Omega, R_g=10\,\text{k}\Omega$

Speaker notes:
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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## Where Each Topology Shines
	Inverting:
	• Precise gains, easy summing, virtual ground node
	Non-inverting:
	• High input impedance, sensor buffering
	Follower:
	• Isolation between stages

Pick based on source impedance and required gain.

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## Wrap-Up
	• Ideal rules simplify analysis
	• Negative feedback sets the gain and linear region
	• Open-loop op-amps saturate—use comparators for switching

Thank you! Questions?