Unit 5: Operational Amplifiers and Applications

I. Orientation: The Operational Amplifier

The operational amplifier (op-amp) is a high-gain, direct-coupled differential voltage amplifier, introduced in integrated form in the 1960s (Fairchild μA741, 1968). It amplifies the difference between two input voltages and forms the building block of most linear analog signal processing.

• Differential input: Two inputs — inverting (−) and non-inverting (+); output responds to Vout = A(V+ − V−), where A is the open-loop gain.
• Open-loop gain (A): Very large, typically 10⁵–10⁶ (100 dB) for the 741; makes negative feedback the governing design principle.
• Power supply: Usually dual supply ±Vcc (e.g. ±15 V); output swings between saturation limits near the rails.
• Feedback dependence: Almost all applications use negative feedback so that circuit behaviour is set by external passive components, not by the unpredictable internal gain.
• Golden rules (with negative feedback): (1) No current flows into the inputs; (2) the op-amp adjusts its output to force V+ = V−.

II. The 741 Op-Amp — Internal Structure and Terminals

A. Block Diagram

The 741 is organised as three cascaded stages that convert a differential input into a low-impedance single-ended output.

• Input stage: Dual differential amplifier with current-mirror active load; provides high input impedance, high CMRR, and most of the voltage gain.
• Intermediate stage: A second differential/level-shifting gain stage that adds gain and shifts the DC level toward zero.
• Output stage: Class-AB complementary emitter-follower (push-pull); gives low output impedance and current drive.
• Bias and compensation: Internal current-mirror biasing plus a 30 pF Miller capacitor for frequency compensation, ensuring stability.

B. Pin Configuration (8-pin DIP)

Standard pinout for the 741 in an 8-pin package.

1  Offset Null      8  NC (No Connection)
2  Inverting In (−) 7  +Vcc
3  Non-inv In (+)   6  Output
4  −Vee             5  Offset Null

• Pins 2, 3: Signal inputs.
• Pins 7, 4: Positive and negative supply.
• Pin 6: Output.
• Pins 1, 5: Offset-null trimming via a potentiometer to cancel input offset voltage.

III. Ideal Behaviour and Non-Ideal Parameters

A. Characteristics of Ideal Op-Amp

An ideal op-amp is the reference model against which real devices are judged.

• Infinite open-loop gain: A = ∞, so a vanishingly small differential input drives the output.
• Infinite input impedance: Zin = ∞; draws zero input current (supports golden rule 1).
• Zero output impedance: Zout = 0; output voltage independent of load.
• Infinite bandwidth: Gain constant at all frequencies.
• Zero offset voltage: Output is zero when both inputs are equal.
• Infinite CMRR and slew rate: Perfect rejection of common signals, instantaneous output response.

B. CMRR (Common-Mode Rejection Ratio)

CMRR measures the amplifier's ability to reject signals common to both inputs while amplifying the difference.

CMRR = Ad / Acm
CMRR(dB) = 20 log10 (Ad / Acm)

• Symbols: Ad = differential gain; Acm = common-mode gain.
• Meaning: High CMRR rejects noise, hum, and interference appearing equally on both leads.
• 741 value: Typically 90 dB (ratio ≈ 31,600) — ideal is infinite.

C. Slew Rate

Slew rate is the maximum rate of change of output voltage, a large-signal limitation caused by finite internal charging current of the compensation capacitor.

SR = dVout/dt |max   (V/µs)

• 741 value: ≈ 0.5 V/µs — modest, causing distortion of fast, large-amplitude signals.
• Full-power bandwidth: f_max = SR / (2π·Vpeak); sets the highest undistorted sine frequency for a given output amplitude.
• Effect: Below slew limit output follows input; above it, sine waves degrade toward triangular shapes.

IV. Differential Amplifier Configurations

The differential amplifier is the input core of the op-amp, amplifying the voltage difference between two nodes.

• Dual-input, balanced-output: Two inputs, output taken between both collectors; highest CMRR, symmetric.
• Dual-input, unbalanced-output: Two inputs, output from one collector to ground; used where single-ended output is needed.
• Single-input, balanced-output: One signal input, output across both collectors.
• Single-input, unbalanced-output: One input, one output; behaves like a phase-splitter/amplifier.
• Common-mode behaviour: A shared emitter resistor (or current source) degenerates common-mode signals, raising CMRR; a constant-current source is preferred for high rejection.

V. Linear Op-Amp Applications

A. Concept of Virtual Ground

Virtual ground explains why the inverting input node behaves as ground without being connected to it.

• Origin: With the non-inverting input grounded and heavy negative feedback, the op-amp forces V− ≈ V+ = 0.
• Consequence: The inverting node sits at 0 V ("virtual") but sources/sinks no current into the op-amp (virtual ground), so all input current flows through the feedback resistor.
• Use: Simplifies analysis of inverting, summing, integrator, and differentiator circuits.

B. Inverting Amplifier

Amplifies and inverts the input, with gain set by two resistors.

Vout = − (Rf / Rin) · Vin

• Symbols: Rin = input resistor, Rf = feedback resistor.
• Derivation: Current Iin = Vin/Rin flows through Rf (virtual ground), giving Vout = −Iin·Rf.
• Input impedance: Equals Rin.

C. Non-Inverting Amplifier

Amplifies without phase inversion; gain always ≥ 1.

Vout = (1 + Rf / Rin) · Vin

• Feature: Very high input impedance (input applied directly to +).
• Example: Rf = 9 kΩ, Rin = 1 kΩ → gain = 10, so 0.2 V input gives 2 V output.

D. Voltage Follower

A unity-gain buffer, Vout = Vin, obtained by setting Rf = 0, Rin = ∞.

• Purpose: Impedance isolation — very high input impedance, very low output impedance.
• Use: Buffers a weak source before driving a low-impedance load without loading the source.

E. Summing Amplifier

Adds several weighted input voltages at the inverting node.

Vout = − Rf (V1/R1 + V2/R2 + V3/R3)

• Virtual ground: Each input current is independent, so inputs do not interact.
• Equal resistors: If R1=R2=R3=Rf, Vout = −(V1+V2+V3) — a true adder.
• Application: Audio mixers, digital-to-analog conversion.

F. Difference Amplifier

Amplifies the difference of two inputs while rejecting common signals.

Vout = (Rf / R1)(V2 − V1)   when R1=R3, R2=Rf

• Balance condition: Resistor matching sets CMRR; mismatch admits common-mode error.
• Application: Sensor bridges, instrumentation front-ends.

G. Differentiator

Produces an output proportional to the rate of change of input.

Vout = − Rf · C · (dVin/dt)

• Operation: Capacitor at input, resistor as feedback; the virtual-ground current is C·dVin/dt.
• Response: Ramp input → constant output; sine input → cosine (90° lead).
• Limitation: High-frequency noise amplified; a series input resistor stabilises it.

H. Integrator

Produces an output proportional to the time integral of the input.

Vout = − (1 / Rin·C) ∫ Vin dt

• Operation: Resistor at input, capacitor as feedback; input current Vin/Rin charges C.
• Response: Constant input → linear ramp; square wave → triangular wave.
• Practical fix: A large resistor across C limits DC gain and prevents saturation from offset drift.

VI. Non-Linear Application: Comparators

A comparator uses the op-amp open-loop (no negative feedback) to compare two voltages and give a saturated digital-like output.

• Basic operation: Vout = +Vsat if V+ > V−; Vout = −Vsat if V+ < V−.
• Zero-crossing detector: Reference at 0 V; output flips as input crosses zero.
• Non-zero reference: A fixed reference voltage on one input sets the switching threshold.
• Schmitt trigger: Adding positive feedback creates two thresholds (hysteresis), giving noise immunity and clean switching:
  
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    VUT = +Vsat·R1/(R1+R2)   VLT = −Vsat·R1/(R1+R2)

• Limitation: The 741 is slow; dedicated comparators (e.g. LM311) switch faster.

VII. Understanding Datasheets of Op-Amps

A datasheet specifies guaranteed and typical parameters needed to select and design with a device.

• Absolute maximum ratings: Supply voltage, input differential voltage, power dissipation, temperature — never to be exceeded.
• Electrical characteristics: Listed as min/typ/max at stated conditions:
  • Input offset voltage (Vio): ~1–6 mV for 741; error added at output.
  • Input bias & offset current: Small DC currents into inputs (~80 nA bias for 741).
  • Large-signal voltage gain: Open-loop gain, e.g. 200 V/mV.
  • CMRR and PSRR: Rejection of common-mode and supply variations.
  • Slew rate and gain-bandwidth product (GBW): Dynamic limits (741 GBW ≈ 1 MHz).
• Package and pin diagram: DIP, SOIC, TO-99 outlines with pin assignments.
• Typical characteristic curves: Gain vs frequency, output swing vs load, aiding worst-case design.