Operational Amplifiers Tutorials Series
http://ingenuitydias.blogspot.com/2014/06/operational-amplifiers-tutorials-series.html
where:V+: non-inverting input
V−: inverting input
Vout: output
VS+: positive power supply
VS−: negative power supply
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Operation
The amplifier's differential inputs consist of a non-inverting input (+) with voltage V+ and an inverting input (–) with voltage V−; ideally the op-amp amplifies only the difference in voltage between the two, which is called the differential input voltage. The output voltage of the op-amp Vout is given by the equation:
where AOL is the open-loop gain of the amplifier (the term "open-loop" refers to the absence of a
feedback loop from the output to the input).
An operational amplifier (called op-amp) is a specially-designed amplifier in bipolar or CMOS (or Bi-CMOS) with the following typical characteristics:
- Very high gain (10,000 to 1,000,000)
- Differential input
- Very high (assumed infinite) input impedance
- Single ended output
- Very low output impedance
- Linear behaviour (within the range of VNEG < Vout < VPOS
Op-amps are used as generic “black box” building blocks in much Analog electronic design
- Amplification
- Analog filtering
- Buffering
- Threshold detection
An op-amp is usually comprised of at least three different amplifier stages
–Differential amplifier input stage with gain a1(v+ - v-) having inverting & non-inverting inputs
–Stage 2 is a “Gain” stage with gain a2 and differential or singled ended input and output
–Output stage is an emitter follower (or source follower) stage with a gain = ~1 and single-ended output with a large current driving capability
–The saturation limits of v0 are equal VPOS & VNEG
–If (v+ - v-) is slightly positive, v0 saturates at VPOS; if (v+ - v-) is slightly negative, v0 saturates at VNEG
–If v0 is not forced into saturation, then (v+ - v-) must be very near zero and the op-amp is in its linear region (which is usually the case for negative feedback use)
–The input resistance can be considered infinite allowing the assumption of zero input currents
–The output resistance can be considered to be zero, which allows vout to equal the internal voltage v0
•The idealized circuit model of an op-amp is shown at the left-bottom figure
•The transfer characteristic is shown at the left-top
•Op-amps are typically used in negative feedback configurations, where some portion of the output is brought back to the negative input v-
–Stage 2 is a “Gain” stage with gain a2 and differential or singled ended input and output
–Output stage is an emitter follower (or source follower) stage with a gain = ~1 and single-ended output with a large current driving capability
*Simple Op-Amp Model:
–Two supplies VPOS and VNEG are utilized and always assumed (even if not explicitly shown)
–An input resistance rin (very high)
–An output resistance rout (very low) in series with output voltage source vo
–Linear Transfer function is vo = a1 a2(v+ - v-) = Ao(v+ - v-) where Ao is open-loop gain
–vo is clamped at VPOS or VNEG if Ao (v+ - v-) > VPOS or < VNEG, respectively
Ideal Op-amp Approximation
Because of the extremely high voltage gain, high input resistance, and low output resistance of an op-amp, we use the following ideal assumptions:
–An input resistance rin (very high)
–An output resistance rout (very low) in series with output voltage source vo
–Linear Transfer function is vo = a1 a2(v+ - v-) = Ao(v+ - v-) where Ao is open-loop gain
–vo is clamped at VPOS or VNEG if Ao (v+ - v-) > VPOS or < VNEG, respectively
Ideal Op-amp Approximation
Because of the extremely high voltage gain, high input resistance, and low output resistance of an op-amp, we use the following ideal assumptions:
–The saturation limits of v0 are equal VPOS & VNEG
–If (v+ - v-) is slightly positive, v0 saturates at VPOS; if (v+ - v-) is slightly negative, v0 saturates at VNEG
–If v0 is not forced into saturation, then (v+ - v-) must be very near zero and the op-amp is in its linear region (which is usually the case for negative feedback use)
–The input resistance can be considered infinite allowing the assumption of zero input currents
–The output resistance can be considered to be zero, which allows vout to equal the internal voltage v0
•The idealized circuit model of an op-amp is shown at the left-bottom figure
•The transfer characteristic is shown at the left-top
•Op-amps are typically used in negative feedback configurations, where some portion of the output is brought back to the negative input v-
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