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+# Opamps Design
+---
+
+# 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.
+---
+
+## 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”).
+
+---
+
+## Ideal opamp
+/assets/ideal.png
+size: contain
+---
+
+## 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.
+
+---
+
+## 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.
+
+---
+
+## 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 $v_{out} = -\dfrac{R_f}{R_{in}} v_{in}$.
+
+---
+
+## 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 $v_{out}$.
+
+---
+
+## 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.
+
+---
+
+## 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.
+
+---
+
+## 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 $v_+ \approx v_-$.
+
+---
+
+## 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.
+
+---
+
+## 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.
+
+---
+
+## 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: $f_{-3\text{dB}}\approx \dfrac{\text{GBW}}{G}$.
+
+---
+
+## 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.
+
+---
+
+## 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?
+
+
+
+