Operational Amplifiers
An operational amplifier or op-amp is a very high-gain amplifier which has two inputs, one inverting (-) and one non-inverting (+). The output voltage is the difference between the + and - inputs, multiplied by the open-loop gain.
The amplifier's output can be single-ended or, less often, differential. Circuits using op-amps almost always employ negative feedback. Because the op-amp has such high gain, the behavior of the amplifier is amost completely determined by the feedback elements.
The op-amp was developed in 1965 by Mr. Robert Widlar at Fairchild Semiconductors Laboratories. Originally, op-amps were so named because they were used to model the basic mathematical operations (addition, subtraction, integration, differentiation, and so on) in electronic analog computers. In this sense a true operational amplifier is an ideal circuit element.
The ideal op-amp has an infinite open-loop gain, infinite bandwidth, infinite input impedances, zero output impedance and zero noise, as well as zero input offset (exactly 0 V out when both inputs are exactly equal) and no thermal drift.
Modern integrated circuit MOSFET op-amps approximate closer and closer to these ideals in limited-bandwidth, large-signal applications at room temperature. The operational amplifier is arguably the most useful single device in analog electronic circuitry.
With only a handful of external components, it can be made to perform a wide variety of analog signal processing tasks.
Modern op-amps are normally built as an integrated circuit, though occasionally with discrete transistors, and generally have uniform parameters with standardized packaging and power supply needs. Op-amps have many uses in electronics.
One key to the usefulness of these little circuits is in the engineering principle of feedback, particularly negative feedback, which constitutes the foundation of almost all automatic control processes.
The principles presented here in operational amplifier circuits, therefore, extend well beyond the immediate scope of electronics.
In terms of construction, op-amps are based on transistors' amplification (either FET or BJT), and each op-amp contains few tens or hundreds of them. However, an op-amp is one functional, complex unit block, and it has many particular characteristics.
Most single, dual and quad op-amps available have a standardised pinout which permits one type to be substituted for another without wiring changes. A specific op-amp may be chosen for its open loop gain, bandwidth, noise performance, input impedance, power consumption, or a compromise between any of these factors.
Operational Amplifiers can be a tough one to explain, because the topic is quite complex, but
it is also extremely important and it requires proper attention. We will use the classic μA741 op-amp for
example and simulation models.
The following minimal structure is needed to present (generally) Operational Amplifiers:
1. Operational Amplifier specifications
2. Summing Amplifier
3. Noninverting Amplifier
4. Voltage Follower
5. Difference Amplifier
6. Integrator Amplifier
7. Differentiator Amplifier
8. Logarithmic Amplifier
9. Comparator Amplifier
10. Active filters
11. Other Operational Amplifier circuits
OPERATIONAL AMPLIFIER SPECIFICATIONS
If you download the Data Sheet of μA741 you will
discover nothing complicated in there: just lists of specifications and few graphs.
An op-amp has the following main characteristics:
1. High Voltage Gain, noted with Av, and having 103..109 values
2. High input impedance; the ideal case is Zi --> ∞ ohms (Input Impedance tends to reach infinite value)
3. Wide Bandwidth
4. Low output impedance; Zo --> 0 ohms
Let's take a closer look at the μA741 using few common schematic models.
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Fig 1: μA741 pin names assignment
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Fig 2: External (virtual) ground reference Model |
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Fig 3: Inverted op-amp with Feedback; model used to calculate op-amp performance |
GENERAL OP-AMP SPECIFICATION, DATA AND FORMULAS
Input Offset Voltage the op amp will produce an output even when the input pins are at exactly the same voltage. For circuits which require precise DC operation, this effect must be compensated for by adding a little input offset voltage in order to have perfect 0 V output.
Most commercial op-amps provide an offset pin for this purpose. According to the Data Sheet, the Input Offset Voltage for μA741 is 1 mV, on average.
Input Offset Current
Normally, the two input currents should be equal when the output is 0 V. However, there is a slight
imbalance, and for μA741 it takes about 20 nA to compensate--which is negligible in most cases.
Input Bias Current
This is the DC current needed at the amplifier input terminal to establish operation in the linear region a small amount of current (typically ~10nA) into the input pins is required for proper operation. This effect is aggravated by the fact that this current is mismatched slightly between the input pins (i.e., input offset current). This effect is usually important only for very low power circuits.
For the Inverted Feedback circuit presented above,
Input Bias Current Ib is: Ib (appx.) = Vo / Rf
Slew Rate
The rate of change of the output voltage is limited
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SR = dV / dT |
Gain Bandwidth Product
We have seen slew rate limits the maximum frequency. In addition, we have the capacitive reactance that limits
the maximum frequency. So remember the formula used to calculate capacitive reactance:
Xc = 1 / 2*π*f*C
with f being the frequency and C the capacitance
The higher is the frequency the smaller is Xc. In
addition we have:
Av = (Rc || Xc) / Re (from input impedance Zi = 2*β*Re)
with Rc being the AC collector resistance of the op-amp input transistor
|| means: in parallel with
Re is the AC emitter resistance of the op-amp input transistor
Based on values particular to each op-amp type, the Av(f) graph is built, and it is named Baude Diagram.
One decibel is defined as: 1 db = 20 log(Vo/Vi) in this case log is
base 10
The decibel notation allows us to express Av in decibels, when the frequency increases ten times, fx
= f * 10, means Voltage Gain decreases ten times: Avx = Av / (-20 db) with x marking the
new value. In other words, Voltage Gain (Av) is inversely proportional to frequency by a factor of
10.
When Av = 1 (at 0 db) the frequency limit is 1 MHz (for μA741). That 1 MHz value is named "Small-Signal Unity Gain Frequency (Ft)". However, sometimes
another parameter is given in Data Sheets named "Transient Response Rise Time (Tr)",
and it is defined as the time it takes a waveform to raise from 10% to 90% of the final
amplitude.
Unity Gain Frequency Bandwidth (BW) is calculated with: BW
= 0.35 / Tr
The Gain Bandwidth Product is: GBP = BW * Av
with Av being the closed-loop (feedback) Voltage Gain of the op-amp circuit
BW = GBP / Av
BW = 1 MHz / 100 = 10 kHz for μA741
Power Supply and virtual ground
As already mentioned, the ground is virtual (related to) for (some) op-amps, and this is an important
concept. We relate all voltages and currents formulas to that virtual ground.
For most op-amps we need dual power supplies: one negative and one positive. The virtual ground is
between the two supplied voltages. Some models require only one power supply, and the ground
connection. This facilitates working with op-amps, and the formulas used remain the same
The power supply pins (VS+ and VS-) can be labeled many different ways. For FET based op-amps, the positive, common drain supply is labeled VDD and the negative, common source supply is labeled VSS. For BJT based op-amps, the VS+ pin becomes VCC and VS- becomes VEE.
They are also sometimes labeled VCC+ and VCC-, or even V+ and V-, in which case the inputs would be labeled differently. The function remains the same. Often these pins are left out of the diagram for clarity, and the power configuration is described or assumed from the circuit.
NOTE:
In all schematics/circuits presented here the power rails, (V+) and (V-) pins to μA741, are not shown but they do need
to be wired.
Other Characteristics
When connected in a negative feedback configuration, the op-amp will tend to output whatever voltage is necessary to make the input voltages equal. This, and the high input impedance, are sometimes called the two "golden rules" of op-amp design (for circuits that use feedback):
The input voltages will be equal to each other
Example:
Av = Vo / Vi
for μA741 we have:
Vi = Vo / Av = 10 V / 200000 = 50 uV (negligible value)
No current will flow in or out the inputs
Example:
Ii = Vi / Zi
for μA741 we have:
Ii = 50 uV / 2Mohms = 25 pA (negligible value)
DC Behaviour
Open-loop gain is defined as the amplification from input to output without any feedback applied. For most practical calculations, the open-loop gain is assumed to be infinite; in reality, however, it is limited by the amount of voltage applied to power the operational amplifier, i.e. Vs+ and Vs- in the above diagram.
Typical devices exhibit open loop DC gain ranging from 100,000 to over 1 million. This allows the gain in the application to be set simply and exactly by using negative feedback. Of course theory and practice differ, since op-amps have limits that the designer must keep in mind and sometimes work around.
AC behaviour
The op-amp gain calculated at DC does not apply at higher frequencies. This effect is due to limitations within the op-amp itself, such as its finite bandwidth, and to the AC characteristics of the circuit in which it is placed. The best known stumbling-block in designing with op-amps is the tendency for the device to resonate at high frequencies, where negative feedback changes to positive feedback due to parasitic lowpasses.
Typical low cost, general purpose op-amps exhibit a gain bandwidth product of a few MHz. Specialty and high speed op-amps can achieve gain bandwidth products of hundreds of MHz. For very high-frequency circuits, a modified form of op-amp called the current-feedback operational amplifier is often used.
Op-amp limitations
Although the design of most op-amp circuits relies on the "golden rules" above, designers should also be aware that no real op-amp can match these characteristics exactly. Listed below are some of the limitations of real op-amps, as well as how this affects circuit design.
DC imperfections:
Finite gain - the effect is most pronounced when the overall design attempts to achieve gain close to the inherent gain of the op-amp.
Finite input resistance - this puts an upper bound on the resistances in the feedback circuit.
Nonzero output resistance - important for low resistance loads. Except for very small voltage output, power considerations usually come into play first.
AC imperfections:
Finite bandwidth - all amplifiers have a finite bandwidth. However, this is more pronounced in op amps, which use frequency compensation to avoid unintentionally producing positive feedback.
Input capacitance - most important for high frequency operation.
Nonlinear imperfections:
Saturation - output voltage is limited to a peak value slightly less than the power supply voltage.
Slew rate - the rate of change of the output voltage is limited.
Power considerations:
Limited output power - if high power output is desired, an op-amp specifically designed for that purpose must be used. Most op-amps are designed for lower power operation.
Short circuit protection - this is more a feature than a limitation, although it does put limits on design. Most commercial op-amps shut off when the load resistance is below a specified level.
Internal circuitry
Although it is useful and easy to treat the op-amp as a black box with a perfect input/output characteristic, it is important to understand the inner workings, so that one can deal with problems that will arise due to internal parasitic capacitances, etc.
Though designs vary between products and manufacturers, all op-amps have basically the same internal structure, which consists of three stages:
Differential amplifier
Input stage - provides low noise amplification, high input impedance, usually a differential output
Voltage amplifier
Provides high voltage gain, a single-pole frequency rolloff, usually single-ended output
Output amplifier
Output stage - provides high current driving capability, low output impedance, current limiting and short circuit protection circuitry
SUMMING AMPLIFIER
The summing Op-Amp circuit performs mathematical operation of addition.
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Fig 5: Summing Op-Amp |
The summing Op-Amp schematic is used for DC and for AC voltages/currents as well. Because each input voltage is dropped on its resistors, there is no signal mixing/distortion.
The Averaging Op-Amp schematic is a particular case. Each input
resistor is equal to R,
and Rf = Ri / N
Where N is the number of input resistors
Considering three inputs we have:
Vo = -Ri/3 * 1/Ri * (V1 + V2 + V3) = -(V1+V2+V3) / 3
NON-INVERTING AMPLIFIER
Op-Amps can be inverting or noninverting. We have looked at the inverting circuit; time has come to look at the noninverting one.
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Fig 6: Noninverting Op-Amp |
There is no negative sign in the above Av formula. That means, there is no phase inversion, and Voltage Gain (Av) is never less than unity (1).
The Input Impedance of the noninverting schematic is the impedance of the op-amp itself, which is very high.
VOLTAGE FOLLOWER
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Fig 7: Voltage Follower |
This is a very simple circuit which duplicates the input DC or AC signal, with unity amplification.
Due to the very high input impedance this circuit isolates the output. In addition, there is no phase shift, hence the output follows exactly the input. This is a safe input buffer circuit.
DIFFERENCE AMPLIFIER
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Fig 8: Difference Amplifier |
The Difference Amplifier circuit and calculations presented above are also used in Instrumentation Amplifier schematics.
INTEGRATOR AMPLIFIER
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Fig 9: Square-wave Integrator The output is: Vo = (Vipp*Tdc) / (Ri*C) Tdc = duty cycle (50% in this case) |
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Fig 10: Sine-wave Integrator This circuit is perfectly similar to the one above. Only the input signal is changed to sine-wave. In this case the output is: Vo = Vipp / 2*π*f*Ri*C Due to capacitance, we have a lagging phase shift of up to 90 degrees (PI/2) |
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DIFFERENTIATOR AMPLIFIER
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Fig 11: Sine-wave differentiation
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Fig 12: Square-wave
differentiation The derivation of the square-wave is obvious
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Fig 13: Triangle-wave
differentiation |
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LOGARITHMIC AMPLIFIER
For the analog logarithmic schematic the output is proportional to the logarithm of the input signal. The
antilogarithm performs the reverse of the logarithm. No graphs are provided, because tuning these circuits
(finding the right values for their components) is very tough.
The good news is, there are few ICs specially designed to perform the log and antilog functions, with all needed
biasing components built-in.
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Fig 14: Logarithmic amplifier This is a simplified schematic of the practical-implementation circuit. |
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Fig 15: Antilogarithmic amplifier |
COMPARATOR AMPLIFIER
Comparator amplifier circuits are greatly used in hardware design. Here we show a schematic with feedback and memory (hysterensis).
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Fig 16: Comparator with Feedback and
Hysterensis (Memory) This is a "zero crossing" type of comparator |
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ACTIVE FILTERS
This topic is presented in - Filters.
OTHER OPERATIONAL AMPLIFIER CIRCUITS
There are very many types of op-amp based circuits, a few examples being:
- Sine-wave oscillator
- Square-wave oscillator
- Voltage regulators
- Voltage-to-current and current-to-voltage converters
- Sample and hold circuits
- Current differencing amplifier (CDA)
- Programmable Operational Amplifiers
