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Lecture 9. Op Amps I • What is an Op Amp? • Ideal Op Amps • Applications • Examples 1 What is an Op Amp? • Op Amp is short for operational amplifier. • An operational amplifier is modeled as a voltage controlled voltage source. • An operational amplifier has a very high input impedance and a very high gain. • It has usually differential inputs and a single output. 2 Use of Op Amps • Op amps can be configured in many different ways using resistors and other components. • Amplifiers provide gains in voltage or current. • Op amps can convert current to voltage. • Op amps can provide a buffer between two circuits. • Op amps can be used to implement integrators and differentiators. • Lowpass and bandpass filters. 3 Applications of Op Amps • • • • Amplifiers provide gains in voltage or current. Op amps can convert current to voltage. Op amps can provide a buffer between two circuits. Op amps can be used to implement integrators and differentiators. 4 The Op Amp Symbol High Supply Non-inverting input Inverting input + Output Ground Low Supply 5 The Op Amp Model – Voltage Dependent Source Non-inverting input v+ + Rin Inverting input v- vo + - - A(v+ -v- ) 6 Typical Op Amp • The input resistance Rin is very large (practically infinite). • The voltage gain A is very large (practically infinite). Non-inverting input v+ + Rin Inverting input v- vo + - - A(v+ -v- ) 7 “Ideal” Op Amp • • • • The input resistance is infinite. The gain is infinite. The op amp is in a negative feedback configuration. Infinite input resistance means the current into the inverting input is zero: i- = 0 • Infinite gain means the difference between v+ and v- is zero: v+ - v- = 0 8 The Basic Inverting Amplifier R2 R1 Vin + - + + Vout - 9 Solving the Amplifier Circuit Nodal Analysis: R2 i2 R1 i1 i- i1 + i2 + i-=0 10 Solving the Amplifier Circuit i 0 vin v vin i1 R1 R1 vout v vout i2 R2 R2 i1 + i2 + i-=0 vin vout 0 R1 R2 11 Solving the Amplifier Circuit Solve for vout vout R1 vin R2 Amplifier gain: vout R2 G vin R1 12 How to solve Op Amp Circuit? • Nodal analysis or other methods to solve for the output voltage in terms of the input(s). • Keep in mind that the ideal op amp model leads to the following conditions: i- = 0 v+ = v- 13 Where is the Feedback? R2 R1 Vin + - + + Vout - 14 The Non-Inverting Amplifier + + vin + - vout R2 R1 - 15 Nodal Analysis: Finding the nodes + + vin + - ii1 i2 vout R2 R1 - 16 Nodal Analysis: Apply KCL i 0 v vin i1 R1 R1 vout v vout vin i2 R2 R2 17 Nodal Analysis: Solve for Vout vin vout vin 0 R1 R2 vout R2 vin 1 R1 18 A Mixer Circuit R1 v1 + Rf R2 - v2 + - + + vout - 19 Nodal Analysis: Finding the nodes R1 i1 v1 + R2 i 2 v2 + - Rf if i- + + vout - 20 Nodal Analysis: Apply KCL v1 v v1 i1 R1 R1 v2 v v2 i2 R2 R2 i 0 vout v vout if Rf Rf 21 Nodal Analysis: Solve for Vout v1 v 2 vout 0 R1 R2 R f vout Rf R1 v1 Rf R2 v2 22 Class Examples • Seeing atoms with STM 1 nA 23 Class Examples • Solar cell 1 nA A circuit constructed for measuring current from the solar cell. The first Op Amp is the current-to-voltage converter and the second op Amp inverts the voltage. 24