Operational Amplifier OpAmp

Overview Amplifier impedance The operational amplifier Ideal op-amp Negative feedback Applications Amplifiers Summing/ subtracting circuits

Impedances Why do we care about the input and output impedance? Simplest "black box" amplifier model: ROUT VIN RIN AVIN VOUT The amplifier measures voltage across RIN, then generates a voltage which is larger by a factor A This voltage generator, in series with the output resistance ROUT, is connected to the output port. A should be a constant (i.e., gain is linear)

Impedances Attach an input - a source voltage VS plus source impedance RS RS ROUT RIN VOUT VIN AVIN VS Note the voltage divider RS + RIN. VIN=VS(RIN/(RIN+RS) We want VIN = VS regardless of source impedance So want RIN to be large. Q: What would be the input impedance of an ‘ideal amplifier’?  The ideal amplifier has an infinite input impedance

Impedances Attach a load - an output circuit with a resistance RL RS ROUT RIN RL VIN AVIN VOUT VS Note the voltage divider ROUT + RL. VOUT=AVIN(RL/(RL+ROUT)) Want VOUT=AVIN regardless of load We want ROUT to be small. Q: What would be the output impedance of an ‘ideal amplifier’?  The ideal amplifier has zero output impedance

Operational Amplifier Integrated circuit containing ~20 transistors, multiple amplifier stages

Ideal Operational Amplifier Operational amplifier (Op-amp) is made of many transistors, diodes, resistors and capacitors in integrated circuit technology. Ideal op-amp is characterized by: Infinite input impedance Infinite gain for differential input Zero output impedance Infinite frequency bandwidth

Operational Amplifier An op amp is a high voltage gain, DC amplifier with high input impedance, low output impedance, and differential inputs. Positive input at the non-inverting input produces positive output Positive input at the inverting input produces negative output.

741 Op Amp IC

A component-level diagram of the common 741 op-amp A component-level diagram of the common 741 op-amp. Dotted lines outline: current mirrors (red); differential amplifier (blue); class A gain stage (magenta); voltage level shifter (green); output stage (cyan).

Operational Amplifier IC Product DIP-741 Dual op-amp 1458 device Operational Amplifier

A small-scale integrated circuit, the 741 op-amp shares with most op-amps an internal structure consisting of three gain stages: 1. Differential amplifier (outlined blue) — provides high differential amplification (gain), with rejection of common-mode signal, low noise, high input impedance

2. Voltage amplifier (outlined magenta) — provides high voltage gain, a single-pole frequency roll-off, and in turn drives the 3. Output amplifier (outlined cyan and green) — provides high current gain (low output impedance), along with output current limiting, and output short-circuit protection. Additionally, it contains current mirror (outlined red) bias circuitry and a gain-stabilization capacitor (30 pF).

Op Amp Equivalent Circuit vd = v2 – v1 A is the open-loop voltage gain v2 v1 Voltage controlled voltage source

Operational Amplifier Can model any amplifier as a "black-box" with a parallel input impedance Rin, and a voltage source with gain Av in series with an output impedance Rout.

Ideal op-amp Place a source and a load on the model + vout RL RS So the equivalent circuit of an ideal op-amp looks like this: Infinite internal resistance Rin (so vin=vs). Zero output resistance Rout (so vout=Avvin). "A" very large iin=0; no current flow into op-amp

Ideal vs. Real op-amps!

Symbols for Ideal and Real Op Amps uA741 LM111 LM324

Ideal Vs Practical Op-Amp Open Loop gain A  105 Bandwidth BW 10-100Hz Input Impedance Zin >1M Output Impedance Zout 0  10-100  Output Voltage Vout Depends only on Vd = (V+V) Differential mode signal Depends slightly on average input Vc = (V++V)/2 Common-Mode signal CMRR 10-100dB Ref:080114HKN Operational Amplifier

Typical Op Amp Parameters Variable Typical Ranges Ideal Values Open-Loop Voltage Gain A 105 to 108 ∞ Input Resistance Ri 105 to 1013 W ∞ W Output Resistance Ro 10 to 100 W 0 W Supply Voltage Vcc/V+ -Vcc/V- 5 to 30 V -30V to 0V N/A

Almost Ideal Op Amp Ri = ∞ W Ro = 0 W Usually, vd = 0V so v1 = v2 Therefore, i1 = i2 = 0A Ro = 0 W Usually, vd = 0V so v1 = v2 The op amp forces the voltage at the inverting input terminal to be equal to the voltage at the noninverting input terminal if there is some component connecting the output terminal to the inverting input terminal. Rarely is the op amp limited to V- < vo < V+. The output voltage is allowed to be as positive or as negative as needed to force vd = 0V.

Many Applications, e.g., Amplifiers Adders and subtractors Integrators and differentiators Clock generators Active Filters Digital-to-analog converters

Applications Audio amplifiers Instrumentation amplifiers Speakers and microphone circuits in cell phones, computers, mpg players, boom boxes, etc. Instrumentation amplifiers Biomedical systems including heart monitors and oxygen sensors. Power amplifiers Analog computers Combination of integrators, differentiators, summing amplifiers, and multipliers

Applications Originally developed for use in analog computers:

Using op-amps Power the op-amp and apply a voltage Works as an amplifier, but: No flexibility (A~105-6) Exact gain is unreliable (depends on chip, frequency and temp) Saturates at very low input voltages (Max vout=power supply voltage) To operate as an amp, v+-v-<VS/A=12/105 so v+≈v- In the ideal case, when an op-amp is functioning properly in the active region, the voltage difference between the inverting and non-inverting inputs≈0

Voltage Transfer Characteristic Range where we operate the op amp as an amplifier. vd

Inverting Apmlifier

Non-inverting amplifier

Noninverting Amplifier

When A is very large: >>1 Take A=106, R1=9R, R2=R >>1 Gain now determined only by resistance ratio Doesn’t depend on A, (or temperature, frequency, variations in fabrication)

Negative feedback: How did we get to stable operation in the linear amplification region??? Feed a portion of the output signal back into the input (feeding it back into the inverting input = negative feedback) This cancels most of the input Maintains (very) small differential signal at input Reduces the gain, but if the open loop gain is ~, who cares? Good discussion of negative feedback here: http://www.allaboutcircuits.com/vol_3/chpt_8/4.html

Why use Negative feedback?: Helps to overcome distortion and non-linearity Improves the frequency response Makes properties predictable - independent of temperature, manufacturing differences or other properties of the opAmp Circuit properties only depend upon the external feedback network and so can be easily controlled

Positive Feedback When we flip the polarization of the op-amp as shown on the figure we will get a positive feedback that saturates the amplifier output. This is not a good idea.

Negative vs. Positive Feedback Familiar examples of negative feedback: Thermostat controlling room temperature Driver controlling direction of automobile Pupil diameter adjustment to light intensity Familiar examples of positive feedback: Microphone “squawk” in sound system Mechanical bi-stability in light switches Fundamentally pushes toward stability Fundamentally pushes toward instability or bi-stability EE 42/100 Fall 2005 Week 8, Prof. White

Operational Amplifier Noninverting amplifier Noninverting input with voltage divider Less than unity gain Voltage follower Ref:080114HKN Operational Amplifier

Operational Amplifier Inverting Amplifier Kirchhoff node equation at V+ yields, Kirchhoff node equation at V yields, Setting V+ = V– yields Notice: The closed-loop gain Vo/Vin is dependent upon the ratio of two resistors, and is independent of the open-loop gain. This is caused by the use of feedback output voltage to subtract from the input voltage. Ref:080114HKN Operational Amplifier

Op amp circuit 1: Voltage follower So vO=vIN or, using equations What's the gain of this circuit?

Op amp circuit 1: Voltage follower (unity buffer amplifier) So vO=vIN or, using equations What's the application of this circuit? Buffer voltage gain = 1 input impedance=∞ output impedance=0 Useful interface between different circuits: Has minimum effect on previous and next circuit in signal chain RS ROUT RIN RL VIN AVIN VOUT VS

Voltage Follower Special case of noninverting amplifier is a voltage follower Since in the noninverting amplifier vo = v1(1+ R2 /R1) vo = v1 so when R2=0 =>

Op amp circuit 2: Inverting Amplifier Signal and feedback resistor, connected to inverting (-) input. v+=v- connected to ground v+ grounded, so:

Op amp circuit 3: Summing Amplifier Same as previous, but add more voltage sources

Operational Amplifier Multiple Inputs Kirchhoff node equation at V+ yields, Kirchhoff node equation at V yields, Setting V+ = V– yields Ref:080114HKN Operational Amplifier

Summing Amplifier Circuit Ra ia if Rf Rb in va + – ib – + + vn – + vo – vb + – ic + vp – superposition ! Rc vc + – in = 0  ia + ib + ic = -if vp = 0  vn = 0 EE 42/100 Fall 2005 Week 8, Prof. White

Summing Amplifier Applications Applications - audio mixer Adds signals from a number of waveforms http://wiredworld.tripod.com/tronics/mixer.html Can use unequal resistors to get a weighted sum For example - could make a 4 bit binary - decimal converter 4 inputs, each of which is +1V or zero Using input resistors of 10k (ones), 5k (twos), 2.5k (fours) and 1.25k (eights)

Another non-inverting amplifier Feedback resistor still to inverting input, but no voltage source on inverting input (note change of current flow) Input voltage to non-inverting input

Differential Amplifier (subtractor) Useful terms: if both inputs change together, this is a common-mode input change if they change independently, this is a normal-mode change A good differential amp has a high common-mode rejection ratio (CMMR)

Amplifies the difference in voltage between its inputs Amplifies the difference in voltage between its inputs. The name "differential amplifier" must not be confused with the "differentiator”