4.5 KiB
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?