Practical considerations
Resistors used in practical solid-state op-amp circuits are typically in the kΩ range. Resistors much greater than 1 MΩ cause excessive thermal noise and make the circuit operation susceptible to significant errors due to bias or leakage currents.
Practical operational amplifiers draw a small current from each of their inputs due to bias requirements and leakage. These currents flow through the resistances connected to the inputs and produce small voltage drops across those resistances. In AC signal applications this seldom matters. If high-precision DC operation is required, however, these voltage drops need to be considered. The design technique is to try to ensure that these voltage drops are equal for both inputs, and therefore cancel. If these voltage drops are equal and the common-mode rejection ratio of the operational amplifier is good, there will be considerable cancellation and improvement in DC accuracy.
If the input currents into the operational amplifier are equal, to reduce offset voltage the designer must ensure that the DC resistance looking out of each input is also matched. In general input currents differ, the difference being called the input offset current, Ios. Matched external input resistances Rin will still produce an input voltage error of Rin·Ios . Most manufacturers provide a method for tuning the operational amplifier to balance the input currents (e.g., "offset null" or "balance" pins that can interact with an external voltage source attached to a potentiometer). Otherwise, a tunable external voltage can be added to one of the inputs in order to balance out the offset effect. In cases where a design calls for one input to be short-circuited to ground, that short circuit can be replaced with a variable resistance that can be tuned to mitigate the offset problem.
Note that many operational amplifiers that have MOSFET-based input stages have input leakage currents that will truly be negligible to most designs.
Power supply imperfections (e.g., power signal ripple, non-zero source impedance) may lead to noticeable deviations from ideal operational amplifier behavior. For example, operational amplifiers have a specified power supply rejection ratio that indicates how well the output can reject signals that appear on the power supply inputs. Power supply inputs are often noisy in large designs because the power supply is used by nearly every component in the design, and inductance effects prevent current from being instantaneously delivered to every component at once. As a consequence, when a component requires large injections of current (e.g., a digital component that is frequently switching from one state to another), nearby components can experience sagging at their connection to the power supply. This problem can be mitigated with copious use of bypass capacitors placed connected across each power supply pin and ground. When bursts of current are required by a component, the component can bypass the power supply by receiving the current directly from the nearby capacitor (which is then slowly charged by the power supply).
Additionally, current drawn into the operational amplifier from the power supply can be used as inputs to external circuitry that augment the capabilities of the operational amplifier. For example, an operational amplifier may not be fit for a particular high-gain application because its output would be required to generate signals outside of the safe range generated by the amplifier. In this case, an external push–pull amplifier can be controlled by the current into and out of the operational amplifier. Thus, the operational amplifier may itself operate within its factory specified bounds while still allowing the negative feedback path to include a large output signal well outside of those bounds.[1]
An inverting amplifier uses negative feedback to invert and amplify a voltage. The Rin,Rf resistor network allows some of the output signal to be returned to the input. Since the output is 180° out of phase, this amount is effectively subtracted from the input, thereby reducing the input into the operational amplifier. This reduces the overall gain of the amplifier and is dubbed negative feedback.[2]
The presence of the negative sign is a convention indicating that the output is inverted. For example, if Rf is 10 000 Ω and Rin is 1 000 Ω, then the gain would be -10 000Ω/1 000Ω, which is -10. [4]
Theory of operation: An Ideal Operational Amplifier has 2 characteristics that imply the operation of the inverting amplifier: Infinite input impedance, and infinite differential gain. Infinite input impedance implies there is no current in either of the input pins because current cannot flow through an infinite impedance. Infinite differential gain implies that both the (+) and (-) input pins are at the same voltage because the output is equal to infinity times (V+ - V-). As the output approaches any arbitrary finite voltage, then the term (V+ - V-) approaches 0, thus the two input pins are at the same voltage for any finite output.
To begin analysis, first it is noted that with the (+) pin grounded, the (-) must also be at 0 volts potential due to implication 2. with the (-) at 0 volts, the current through Rin (from left to right) is given by I = Vin/Rin by Ohm's law. Second, since no current is flowing into the op amp through the (-) pin due to implication 1, all the current through Rin must also be flowing through Rf (see Kirchoff's Current Law). Therefore, with V- = 0 volts and I(Rf) = Vin/Rin the output voltage given by Ohm's law is -Vin*Rf/Rin.
Real op amps have both finite input impedance and differential gain, however both are high enough as to induce error that is considered negligible in most applications.
Amplifies a voltage (multiplies by a constant greater than 1)
The name "differential amplifier" should not be confused with the "differentiator", also shown on this page.
The "instrumentation amplifier", which is also shown on this page, is another form of differential amplifier that also provides high input impedance.
Whenever and , the differential gain is
Used as a buffer amplifier to eliminate loading effects (e.g., connecting a device with a high source impedance to a device with a low input impedance).
A summing amplifer sums several (weighted) voltages:
[edit] Input offset problems
It is important to note that the equations shown below, pertaining to each type of circuit, assume that an ideal op amp is used. Those interested in construction of any of these circuits for practical use should consult a more detailed reference. See the External links and Further reading sections.Resistors used in practical solid-state op-amp circuits are typically in the kΩ range. Resistors much greater than 1 MΩ cause excessive thermal noise and make the circuit operation susceptible to significant errors due to bias or leakage currents.
Practical operational amplifiers draw a small current from each of their inputs due to bias requirements and leakage. These currents flow through the resistances connected to the inputs and produce small voltage drops across those resistances. In AC signal applications this seldom matters. If high-precision DC operation is required, however, these voltage drops need to be considered. The design technique is to try to ensure that these voltage drops are equal for both inputs, and therefore cancel. If these voltage drops are equal and the common-mode rejection ratio of the operational amplifier is good, there will be considerable cancellation and improvement in DC accuracy.
If the input currents into the operational amplifier are equal, to reduce offset voltage the designer must ensure that the DC resistance looking out of each input is also matched. In general input currents differ, the difference being called the input offset current, Ios. Matched external input resistances Rin will still produce an input voltage error of Rin·Ios . Most manufacturers provide a method for tuning the operational amplifier to balance the input currents (e.g., "offset null" or "balance" pins that can interact with an external voltage source attached to a potentiometer). Otherwise, a tunable external voltage can be added to one of the inputs in order to balance out the offset effect. In cases where a design calls for one input to be short-circuited to ground, that short circuit can be replaced with a variable resistance that can be tuned to mitigate the offset problem.
Note that many operational amplifiers that have MOSFET-based input stages have input leakage currents that will truly be negligible to most designs.
[edit] Power supply effects
Although the power supplies are not shown in the operational amplifier designs below, they can be critical in operational amplifier design.Power supply imperfections (e.g., power signal ripple, non-zero source impedance) may lead to noticeable deviations from ideal operational amplifier behavior. For example, operational amplifiers have a specified power supply rejection ratio that indicates how well the output can reject signals that appear on the power supply inputs. Power supply inputs are often noisy in large designs because the power supply is used by nearly every component in the design, and inductance effects prevent current from being instantaneously delivered to every component at once. As a consequence, when a component requires large injections of current (e.g., a digital component that is frequently switching from one state to another), nearby components can experience sagging at their connection to the power supply. This problem can be mitigated with copious use of bypass capacitors placed connected across each power supply pin and ground. When bursts of current are required by a component, the component can bypass the power supply by receiving the current directly from the nearby capacitor (which is then slowly charged by the power supply).
Additionally, current drawn into the operational amplifier from the power supply can be used as inputs to external circuitry that augment the capabilities of the operational amplifier. For example, an operational amplifier may not be fit for a particular high-gain application because its output would be required to generate signals outside of the safe range generated by the amplifier. In this case, an external push–pull amplifier can be controlled by the current into and out of the operational amplifier. Thus, the operational amplifier may itself operate within its factory specified bounds while still allowing the negative feedback path to include a large output signal well outside of those bounds.[1]
[edit] Circuit applications
[edit] Comparator
Main article: Comparator
Compares two voltages and switches its output to indicate which voltage is larger.[edit] Inverting amplifier
An inverting amplifier uses negative feedback to invert and amplify a voltage. The Rin,Rf resistor network allows some of the output signal to be returned to the input. Since the output is 180° out of phase, this amount is effectively subtracted from the input, thereby reducing the input into the operational amplifier. This reduces the overall gain of the amplifier and is dubbed negative feedback.[2]
- Zin = Rin (because V − is a virtual ground)
- A third resistor, of value , added between the non-inverting input and ground, while not necessary, minimizes errors due to input bias currents.[3]
The presence of the negative sign is a convention indicating that the output is inverted. For example, if Rf is 10 000 Ω and Rin is 1 000 Ω, then the gain would be -10 000Ω/1 000Ω, which is -10. [4]
Theory of operation: An Ideal Operational Amplifier has 2 characteristics that imply the operation of the inverting amplifier: Infinite input impedance, and infinite differential gain. Infinite input impedance implies there is no current in either of the input pins because current cannot flow through an infinite impedance. Infinite differential gain implies that both the (+) and (-) input pins are at the same voltage because the output is equal to infinity times (V+ - V-). As the output approaches any arbitrary finite voltage, then the term (V+ - V-) approaches 0, thus the two input pins are at the same voltage for any finite output.
To begin analysis, first it is noted that with the (+) pin grounded, the (-) must also be at 0 volts potential due to implication 2. with the (-) at 0 volts, the current through Rin (from left to right) is given by I = Vin/Rin by Ohm's law. Second, since no current is flowing into the op amp through the (-) pin due to implication 1, all the current through Rin must also be flowing through Rf (see Kirchoff's Current Law). Therefore, with V- = 0 volts and I(Rf) = Vin/Rin the output voltage given by Ohm's law is -Vin*Rf/Rin.
Real op amps have both finite input impedance and differential gain, however both are high enough as to induce error that is considered negligible in most applications.
[edit] Non-inverting amplifier
Amplifies a voltage (multiplies by a constant greater than 1)
- Input impedance
- The input impedance is at least the impedance between non-inverting ( + ) and inverting ( − ) inputs, which is typically 1 MΩ to 10 TΩ, plus the impedance of the path from the inverting ( − ) input to ground (i.e., R1 in parallel with R2).
- Because negative feedback ensures that the non-inverting and inverting inputs match, the input impedance is actually much higher.
- Although this circuit has a large input impedance, it suffers from error of input bias current.
- The non-inverting ( + ) and inverting ( − ) inputs draw small leakage currents into the operational amplifier.
- These input currents generate voltages that act like unmodeled input offsets. These unmodeled effects can lead to noise on the output (e.g., offsets or drift).
- Assuming that the two leaking currents are matched, their effect can be mitigated by ensuring the DC impedance looking out of each input is the same.
- The voltage produced by each bias current is equal to the product of the bias current with the equivalent DC impedance looking out of each input. Making those impedances equal makes the offset voltage at each input equal, and so the non-zero bias currents will have no impact on the difference between the two inputs.
- A resistor of value
- which is the equivalent resistance of R1 in parallel with R2, between the Vin source and the non-inverting ( + ) input will ensure the impedances looking out of each input will be matched.
- The matched bias currents will then generate matched offset voltages, and their effect will be hidden to the operational amplifier (which acts on the difference between its inputs) so long as the CMRR is good.
- Very often, the input currents are not matched.
- Most operational amplifiers provide some method of balancing the two input currents (e.g., by way of an external potentiometer).
- Alternatively, an external offset can be added to the operational amplifier input to nullify the effect.
- Another solution is to insert a variable resistor between the Vin source and the non-inverting ( + ) input. The resistance can be tuned until the offset voltages at each input are matched.
- Operational amplifiers with MOSFET-based input stages have input currents that are so small that they often can be neglected.
[edit] Differential amplifier
Main article: Differential amplifier
The circuit shown is used for finding the difference of two voltages each multiplied by some constant (determined by the resistors).The name "differential amplifier" should not be confused with the "differentiator", also shown on this page.
- Differential Zin (between the two input pins) = R1 + R2 (Note: this is approximate)
The "instrumentation amplifier", which is also shown on this page, is another form of differential amplifier that also provides high input impedance.
Whenever and , the differential gain is
- and
[edit] Voltage follower
Used as a buffer amplifier to eliminate loading effects (e.g., connecting a device with a high source impedance to a device with a low input impedance).
- (realistically, the differential input impedance of the op-amp itself, 1 MΩ to 1 TΩ)
[edit] Summing amplifier
A summing amplifer sums several (weighted) voltages:
- When , and Rf independent
- When
- Output is inverted
- Input impedance of the nth input is Zn = Rn (V − is a virtual ground)
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