Operational amplifier (op-amp)

An operational amplifier (op-amp) is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op-amp produces an output potential (relative to circuit ground) that is typically hundreds of thousands of times larger than the potential difference between its input terminals.

Operational amplifiers had their origins in analog computers, where they were used to do mathematical operations in many linear, non-linear and frequency-dependent circuits. Characteristics of a circuit using an op-amp are set by external components with little dependence on temperature changes or manufacturing variations in the op-amp itself, which makes op-amps popular building blocks for circuit design.

Op-amps are among the most widely used electronic devices today, being used in a vast array of consumer, industrial, and scientific devices. Many standard IC op-amps cost only a few cents in moderate production volume; however some integrated or hybrid operational amplifiers with special performance specifications may cost over $100 US in small quantities. Op-amps may be packaged as components, or used as elements of more complex integrated circuits.

The op-amp is one type of differential amplifier. Other types of differential amplifier include the fully differential amplifier (similar to the op-amp, but with two outputs), the instrumentation amplifier (usually built from three op-amps), the isolation amplifier (similar to the instrumentation amplifier, but with tolerance to common-mode voltages that would destroy an ordinary op-amp), and negative feedback amplifier (usually built from one or more op-amps and a resistive feedback network).

Circuit Notation

The circuit symbol for an op-amp is shown to the right, where:

• V₊: non-inverting input
• V₋: inverting input
• V_out: output
• V_S+: positive power supply
• V_S−: negative power supply

The power supply pins (V_S+ and V_S−) can be labeled in different ways. Often these pins are left out of the diagram for clarity, and the power configuration is described or assumed from the circuit.

OPERATION

The amplifier's differential inputs consist of a V₊ input and a V₋ input, and 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 is given by the equation:

where V₊ is the voltage at the non-inverting terminal, V₋ is the voltage at the inverting terminal and A_OL 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).

The magnitude of A_OL is typically very large—100,000 or more for integrated circuit op-amps—and therefore even a quite small difference between V₊and V₋ drives the amplifier output nearly to the supply voltage. Situations in which the output voltage is equal to or greater than the supply voltage are referred to as saturation of the amplifier. The magnitude of A_OL is not well controlled by the manufacturing process, and so it is impractical to use an operational amplifier as a stand-alone differential amplifier. Without negative feedback, and perhaps with positive feedback for regeneration, an op-amp acts as a comparator. If the inverting input is held at ground (0 V) directly or by a resistor, and the input voltage V_in applied to the non-inverting input is positive, the output will be maximum positive; if V_in is negative, the output will be maximum negative. Since there is no feedback from the output to either input, this is an open loop circuit acting as a comparator. The circuit's gain is just the A_OL of the op-amp.

If predictable operation is desired, negative feedback is used, by applying a portion of the output voltage to the inverting input. The closed loop feedback greatly reduces the gain of the amplifier. When negative feedback is used, the circuit's overall gain and response becomes determined mostly by the feedback network rather than by the op-amp itself. If the feedback network is made of components with relatively constant, stable values, the variability of the op-amp's open loop response does not seriously affect the circuit's performance. The response of the op-amp circuit with its input, output and feedback circuits to an input is characterized mathematically by a transfer function. Designing an op-amp circuit to have a desired transfer function is in the realm of electrical engineering. The transfer functions are important in most applications of op-amps, such as in analog computers. High inputimpedance at the input terminals and low output impedance at the output terminal(s) are particularly useful features of an op-amp.

For example, in a non-inverting amplifier (see the figure on the right) adding a negative feedback via the voltage divider R_f, R_g reduces the gain. Equilibrium will be established when V_out is just sufficient to reach around and "pull" the inverting input to the same voltage as V_in. The voltage gain of the entire circuit is determined by 1 + R_f/R_g. As a simple example, if V_in = 1 V and R_f = R_g, V_out will be 2 V, the amount required to keep V₋ at 1 V. Because of the feedback provided by R_f, R_g this is a closed loop circuit. Its overall gain V_out / V_in is called the closed-loop gain A_CL. Because the feedback is negative, in this case A_CL is less than the A_OL of the op-amp.

Another way of looking at it is to make two relatively valid assumptions.

One, that when an op-amp is being operated in linear (not saturated) mode, the difference in voltage between the non-inverting (+) pin and the inverting (−) pin is so small as to be considered negligible

The second assumption is that the input impedance at both (+) and (−) pins is extremely high (at least several megohms with modern op-amps).

Thus, when the circuit to the right is operated as a non-inverting linear amplifier, V_in will appear at the (+) and (−) pins and create a current i through R_g equal to V_in/R_g. Since Kirchhoff's current law states that the same current must leave a node as enter it, and since the impedance into the (−) pin is near infinity, we can assume the overwhelming majority of the same current i travels through R_f, creating an output voltage equal to V_in + i × R_f. By combining terms, we can easily determine the gain of this particular type of circuit.

CHARACTERISTICS 

Real operational amplifiers suffer from several non-ideal effects:

Finite gain

Open-loop gain is infinite in the ideal operational amplifier but finite in real operational amplifiers. Typical devices exhibit open-loop DC gain ranging from 100,000 to over 1 million. So long as the loop gain (i.e., the product of open-loop and feedback gains) is very large, the circuit gain will be determined entirely by the amount of negative feedback (i.e., it will be independent of open-loop gain). In cases where closed-loop gain must be very high, the feedback gain will be very low, and the low feedback gain causes low loop gain; in these cases, the operational amplifier will cease to behave ideally.

Finite input impedances
The differential input impedance of the operational amplifier is defined as the impedance between its two inputs; the common-mode input impedance is the impedance from each input to ground. MOSFET-input operational amplifiers often have protection circuits that effectively short circuit any input differences greater than a small threshold, so the input impedance can appear to be very low in some tests. However, as long as these operational amplifiers are used in a typical high-gain negative feedback application, these protection circuits will be inactive. The input bias and leakage currents described below are a more important design parameter for typical operational amplifier applications.

Non-zero output impedance
Low output impedance is important for low-impedance loads; for these loads, the voltage drop across the output impedance of the amplifier will be significant. Hence, the output impedance of the amplifier limits the maximum power that can be provided. In configurations with a voltage-sensing negative feedback, the output impedance of the amplifier is effectively lowered; thus, in linear applications, op-amps usually exhibit a very low output impedance indeed. Negative feedback can not, however, reduce the limitations that R_load in conjunction with R_out place on the maximum and minimum possible output voltages; it can only reduce output errors within that range.
Low-impedance outputs typically require high quiescent (i.e., idle) current in the output stage and will dissipate more power, so low-power designs may purposely sacrifice low output impedance.

Input current
Due to biasing requirements or leakage, a small amount of current (typically ~10 nanoamperes for bipolar op-amps, tens of picoamperes for JFET input stages, and only a few pA for MOSFET input stages) flows into the inputs. When large resistors or sources with high output impedances are used in the circuit, these small currents can produce large unmodeled voltage drops. If the input currents are matched, and the impedance looking out of both inputs are matched, then the voltages produced at each input will be equal. Because the operational amplifier operates on the difference between its inputs, these matched voltages will have no effect (unless the operational amplifier has poor CMRR, which is described below). It is more common for the input currents (or the impedances looking out of each input) to be slightly mismatched, and so a small offset voltage (different from the input offset voltage below) can be produced. This offset voltage can create offsets or drifting in the operational amplifier. It can often be nulled externally; however, many operational amplifiers include offset null or balance pins and some procedure for using them to remove this offset. Some operational amplifiers attempt to nullify this offset automatically.

Input offset voltage
This voltage, which is what is required across the op-amp's input terminals to drive the output voltage to zero,^{[6][nb 1]} is related to the mismatches in input bias current. In the perfect amplifier, there would be no input offset voltage. However, it exists in actual op-amps because of imperfections in the differential amplifier that constitutes the input stage of the vast majority of these devices. Input offset voltage creates two problems: First, due to the amplifier's high voltage gain, it virtually assures that the amplifier output will go into saturation if it is operated without negative feedback, even when the input terminals are wired together. Second, in a closed loop, negative feedback configuration, the input offset voltage is amplified along with the signal and this may pose a problem if high precision DC amplification is required or if the input signal is very small.^{[nb 2]}

Common-mode gain
A perfect operational amplifier amplifies only the voltage difference between its two inputs, completely rejecting all voltages that are common to both. However, the differential input stage of an operational amplifier is never perfect, leading to the amplification of these identical voltages to some degree. The standard measure of this defect is called the common-mode rejection ratio(denoted CMRR). Minimization of common mode gain is usually important in non-inverting amplifiers (described below) that operate at high amplification.
Output sink current
The output sink current is maximum current allowed to sink into the output stage. Some manufacturers show the output voltage vs. the output sink current plot, which gives an idea of the output voltage when it is sinking current from another source into the output pin.
Temperature effects
All parameters change with temperature. Temperature drift of the input offset voltage is especially important.

Power-supply rejection
The output of a perfect operational amplifier will be completely independent from ripples that arrive on its power supply inputs. Every real operational amplifier has a specified power supply rejection ratio (PSRR) that reflects how well the op-amp can reject changes in its supply voltage. Copious use of bypass capacitors can improve the PSRR of many devices, including the operational amplifier.

Drift
Real op-amp parameters are subject to slow change over time and with changes in temperature, input conditions, etc.

Noise
Amplifiers generate random voltage at the output even when there is no signal applied. This can be due to thermal noise and flicker noise of the devices. For applications with high gain or high bandwidth, noise becomes a very important consideration.

WELCOME to ELECTROMATE

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      The Electromate blog is a hobby blog page that aims to teach and help people understand the seemingly incomprehensible electronic gadgets in the world today, and also assists people in developing their own devices. To this end, various lectures, workshops, projects as well as competitions throughout the year concerning both analog as well as digital electronics keep the calendar busy and the participants, learning. 

By: ELECTROMATE

The Multiplexers

        Multiplexing is the generic term used to describe the operation of sending one or more signals over a common transmission line at different times and as such, the device we use to do just that is called a Multiplexer.

A multiplexer is a combinational logic circuit design to switch one of several input lines through to one single output line by the application of a control signal. Multiplexers, often shortened to MUX, can be either digital circuits made from high speed logic gates used to switch digital or binary data or they can be analogue using transistors, mosfets or relays to switch one of the voltage or current inputs through to a single output.

Multiplexers also known as selectors because they can “select” each input line, are combinational logic circuits whose output condition either “HIGH” or “LOW” is determined at any time by its input state. In other words, multiplexers are switching circuits that just switch or route signals through themselves, and being a combinational circuit are memoryless as there is no signal feedback path.

The most basic type of multiplexer device is that of a one-way rotary switch as shown.

The rotary switch, also called a wafer switch as each layer of the switch is known as a wafer, is a mechanical device whose input is selected by rotating a shaft. In other words, the rotary switch is a manual switch that you can use to select individual data or signal lines simply by turning its inputs “ON” or “OFF”. So how can we select each data input automatically using a digital device.

The selection of each input line in a multiplexer is contro1led by an additional set of inputs called control lines. Normally, a multiplexer has 2^N input lines and a set of n control or address lines are needed to select one of the 2^N inputs to pass the data to the single output. Note that multiplexers are different in operation to Encoders. Encoders are able to switch an n-bit input pattern to multiple output lines that represent the binary coded (BCD) output equivalent of the active input.

We can build a simple 2-line to 1-line (2-to-1) multiplexer from basic logic NAND gates as shown.

2-input Multiplexer Design

The input A of this simple 2-1 line multiplexer circuit constructed from standard NAND gates acts to control which input ( I₀ or I₁ ) gets passed to the output at Q.

From the truth table we can see that when data select input, A is LOW (logic 0), input I₁ passes its data to the output while input I₀ is blocked. When data select A is HIGH (logic 1), input I₀ is passed to Q while input I₀ is blocked.

So by the application of either a logic “0″ or a logic “1″ at Q we can select the appropriate input with the circuit acting a bit like a single pole double throw (SPDT) switch. Then in this simple example, the 2-input multiplexer connects one of two 1-bit sources to a common output, producing a 2-to-1-line multiplexer and we can confirm this in the following Boolean expression.

Q = A.I₀.I₁ + A.I₀.I₁ + A.I₀.I₁ + A.I₀.I₁

and for our 2-input multiplexer circuit above, this can be simplified too:

Q = A.I₁ + A.I₀

We can increase the number of data inputs to be selected further simply by following the same procedure and larger multiplexer circuits can be implemented using smaller 2-to-1 multiplexers as building blocks. For a 4-input multiplexer we would therefore require two data select lines as 4-inputs represents 2² data control lines give a circuit with four inputs, I₀, I₁, I₂, I₃ and two data select lines A and B as shown.

4-input Multiplexer Design

 

We can see from above that the input which appears at the output Q is the only one selected by the control inputs A and B. The x value in the truth table corresponds to a “don’t care” condition. This means that the particular input can be at either a logic “0″ or a logic “1″ having no effect on the output state.

Then we can show the selection of the data through the 4-input multiplexer as a function of the data select bits as shown.

Adding more control address lines will allow the multiplexer to control more inputs by a value of 2ⁿ control lines, but each control line configuration will connect only ONE input to the output.

The Multiplexer is a very useful combinational logic device allowing multiple data lines to be connected to a single output and as such they can be used in many different applications such as signal routing, data communications and data bus control. In general, a multiplexer with n select lines can select one of 2ⁿ data inputs. Therefore, multiplexers are sometimes referred to as “data selectors”.