Ch. 5 – Operational Amplifiers Ideal Amplifier Symbol Circuit Model vi = input voltage; vo = A vi ; A = amplification or gain Both voltages are with respect to ground Input current is zero input power is zero power amplification is infinite vo is “bare voltage” infinite output power
Improvements: Input resistance Ri; input current ii Output resistance Ro (Thevenin equivalent as seen by load) Real Amplifier Model Has 3 parameters: is the open-circuit amplification
If a source (vs and Rs) and a load (RL) are connected, find the real amplifier gain.
OPERATIONAL AMPLIFIERS: An operational amplifier (or op amp) is an electronic unit that behaves like a voltage-controlled voltage source, and can be used to perform mathematical operations such as addition, subtraction, multiplication, division, differentiation and integration. a) Circuit symbol (ideal) b) pin configuration The five terminals of the op amp are: a) The inverting input, vn (pin 2), b) The non-inverting input, vp (pin 3) c) The output, vo (pin 6), d) The positive power supply, V+, pin 7. e) The negative power supply, V-, pin 4.
The five terminals of the op amp are: a) The inverting input, vn (pin 2), b) The non-inverting input, vp (pin 3) c) The output, vo (pin 6), d) The positive power supply, V+, pin 7. e) The negative power supply, V-, pin 4. Real op amp – typical values The differential input voltage vd (or vi) is vd = vp -vn. The output voltage is given by vo = A vd = A (vp – vn)
Ideal Op AMP with NEGATIVE FEEDBACK Analysis Technique Assumptions: and Results: Therefore, the input terminals of an ideal op amp are both a short circuit and an open-circuit. Example: a) Use the ideal op amp technique to predict vo.
Compare a) with a real op amp with Ri = 105, A = 104, and Ro =0.
OP AMP Circuits 1. Voltage Follower - See example above.
2. Basic Inverting Amplifier
Ex. 3 Determine vo. Ans. -12 V
3. Basic Non-inverting Amplifier
Example 4. Answer: 7 V
4. Current-to-voltage converter
5. Voltage-to-current converter
6. Summing Circuit
Example 5. Find vo and io. Ans: -3.8, -1.425
7. Difference Amplifier
Ex. 6. Design an op-amp circuit with inputs v1 and v2 such that vo = -5v1 + 3v2 a) Use a difference amplifier
b) Use a cascaded op amp circuit
8. Op-amp Integrator
9. Op-amp Differentiator
Cascaded op amp Circuits Cascade connection - head-to-tail arrangement of two or more circuits such that the output of one is the input of the next. Given: v1=2V; v2=1.5V Find: vo Ans: 9V