Basics of Operational Amplifiers CHAPTER 9 Basics of Operational Amplifiers

OBJECTIVES Describe and Analyze: Op-Amp Basics Feedback Inverting Amplifiers Non-Inverting Amplifiers Comparators Troubleshooting

Introduction Op-Amps have: Differential Inputs: (+) & (-) High “Open Loop” Gain: AOL > 100,000 (Open-loop means without feedback. More on that later.) High Input Impedance: Zin > 1 Meg Low Output Impedance: Zout  0

Introduction Some Facts about Op-Amps: Op-amps are the most commonly used linear ICs. An IC package can have 1, 2, 4, or more op-amps. Op-amps come in many varieties based on parameters such as bandwidth, cost, and transistor type (BJT, JFET, MOSFET).

Op-Amp Basics Analysis can be based on two approximations: No current flows into or out of the input pins The voltage across the input pins is zero

The front-end of an Op-Amp is a differential amplifier Op-Amp Basics The front-end of an Op-Amp is a differential amplifier

Simplest circuit, illustrates use of negative feedback Voltage Follower Simplest circuit, illustrates use of negative feedback

Non-Inverting Amplifier Av = 1 + (Rf / Ri)

Non-Inverting Amp Gain equation derived as follows: Vin applied to (+) input means V(+) = Vin zero difference across inputs implies V(-) = V(+) V(-) = V(+) implies V(-) = Vin Iin = 0 implies V(-) = Vin = [Ri / (Ri + Rf)]  Vout which leads to Vin / Vout = Ri / (Ri + Rf) which leads to Vout / Vin = Av = (Ri + Rf) / Ri which is the same as Av = 1 + Rf / Ri

Non-Inverting Amp An example calculation: Find Vout if Vin = 1 Volt DC, Rf = 10k, Ri = 5k Find voltage at (-) input Av = 1 + Rf / Ri = 1 + 10k / 5k = 1 + 2 = 3 Vout = Av  Vin = 3  1V = 3 Volts DC V(-) = V(+) = 1 Volt DC

Negative feedback reduces gain to a useable value

Negative Feedback Besides setting the gain, negative feedback provides performance improvements such as: Makes Zin higher Makes Zout lower Increases the usable bandwidth Reduces distortion in the op-amp

It looks complicated, but actually it’s not Negative Feedback It looks complicated, but actually it’s not

Negative Feedback We can analyze negative feedback as follows: Some of the output is fed back to the input: Vfb = B  Vout where 0 < B < 1 The signal that gets to the op-amp is the applied input plus the feedback: Vx = Vin + Vfb = Vin + B  Vout But the output is the open-loop gain of the op-amp times the signal that gets to the input: Vout = AOL  Vx = AOL  (Vin + B  Vout) Now we can find closed-loop gain: ACL = Vout / Vin as we will see on the next slide.

Negative Feedback Start with Vout = AOL  (Vin + B  Vout) Then Vout = AOL  Vin + AOL  B  Vout Then Vout – B  AOL  Vout = AOL  Vin Then (1 - B  AOL )  Vout = AOL  Vin Then Vout = [AOL / (1 - B  AOL ) ]  Vin Then Vout / Vin = ACL = AOL / (1 - B  AOL ) Where ACL is the closed-loop gain Now, if B  AOL >> 1 (which is usually the case) then ACL  1 / B where B is set by a resistor ratio.

The Inverting Amplifier Av = - (Rf / Ri) where minus means 180O phase shift

The Inverting Amp Gain equation derived as follows: Vin applied to (-) input through Ri zero difference across inputs implies V(-) = V(+) (+) input grounded implies V(-)  0 (-) input is a “virtual ground” which leads to Iin = Vin / Ri and If = Vout / Rf no current into (-) input implies If = Iin so Vout / Rf = Vin / Rin and Vout / Vin = Rf / Rin If Vin makes Iin flow in, Vout must make If flow out. So Vout has opposite polarity of Vin: Av = -Rf / Ri

The Inverting Amp An example calculation: Find Vout if Vin = 1 Volt DC, Rf = 10k, Ri = 5k Av = - Rf / Ri = - (10k / 5k) = - 2 Vout = Av  Vin = -2  1V = -2 Volts DC

Very small V between inputs gives a binary output Comparators Very small V between inputs gives a binary output

Comparators Some Facts about Comparators: Comparator output is high or low depending on which input has the higher voltage applied to it. An open-loop op-amp can be used as a comparator. Open-loop op-amps go into saturation, and they take a relatively long time to get out of saturation. The output can “chatter” (oscillate high / low) when inputs are equal. Chatter can be cured with hysteresis. There are ICs designed to be comparators. They are better at the job than op-amps.

Troubleshooting Check the power rails: +VCC and –VCC Check if the output is in saturation (usually, saturation is not a good thing). Check the input voltages, knowing that voltage across inputs is supposed to be virtually zero. Check that polarity (phase) of output is the same as input for a non-inverting amplifier. Check that polarity (phase) of output is the opposite input for an inverting amplifier. Check signal levels based on gains (look at the resistor ratios of the feedback loops).