Transconductance (for transfer conductance), also infrequently called mutual conductance , is the electrical characteristic relating the current through the output of a device to the voltage across the input of a device. Conductance is the reciprocal of resistance.
Transadmittance (or transfer admittance ) is the AC equivalent of transconductance.
Transconductance is very often denoted as a conductance, gm, with a subscript, m, for mutual. It is defined as follows:
For small signal alternating current, the definition is simpler:
The SI unit for transconductance is the siemens , with the symbol S, as in conductance.
Transresistance (for transfer resistance), also infrequently referred to as mutual resistance, is the dual of transconductance. It refers to the ratio between a change of the voltage at two output points and a related change of current through two input points, and is denotated as rm:
The SI unit for transresistance is simply the ohm, as in resistance.
Transimpedance (or, transfer impedance ) is the AC equivalent of transresistance, and is the dual of transadmittance.
For vacuum tubes, transconductance is defined as the change in the plate (anode) current divided by the corresponding change in the grid/cathode voltage, with a constant plate (anode) to cathode voltage. Typical values of gm for a small-signal vacuum tube are 1 to 10 mS. It is one of the three characteristic constants of a vacuum tube, the other two being its gain μ (mu) and plate resistance rp or ra. The Van der Bijl equation defines their relation as follows:
Similarly, in field-effect transistors, and MOSFETs in particular, transconductance is the change in the drain current divided by the small change in the gate–source voltage with a constant drain–source voltage. Typical values of gm for a small-signal field-effect transistor are 1 to 30 mS.
Using the Shichman–Hodges model, the transconductance for the MOSFET can be expressed as (see MOSFET § Modes of operation )
where ID is the DC drain current at the bias point, and VOV is the overdrive voltage, which is the difference between the bias point gate–source voltage and the threshold voltage (i.e., VOV ≡ VGS – Vth). [2] : p. 395, Eq. (5.45) The overdrive voltage (sometimes known as the effective voltage) is customarily chosen at about 70–200 mV for the 65 nm process node (ID ≈ 1.13 mA/μm × width) for a gm of 11–32 mS/μm. [3] : p. 300, Table 9.2 [4] : p. 15, §0127
Additionally, the transconductance for the junction FET is given by
where VP is the pinchoff voltage, and IDSS is the maximum drain current.
The gm of bipolar small-signal transistors varies widely, being proportional to the collector current. It has a typical range of 1 to 400 mS. The input voltage change is applied between the base/emitter and the output is the change in collector current flowing between the collector/emitter with a constant collector/emitter voltage.
The transconductance for the bipolar transistor can be expressed as
where IC is the DC collector current at the Q-point, and VT is the thermal voltage, typically about 26 mV at room temperature. For a typical current of 10 mA, gm ≈385 mS. The input impedance is the current gain (β) divided by the transconductance.
The output (collector) conductance is determined by the Early voltage and is proportional to the collector current. For most transistors in linear operation it is well below 100 μS.
A transconductance amplifier (gm amplifier) puts out a current proportional to its input voltage. In network analysis , the transconductance amplifier is defined as a voltage controlled current source (VCCS). These amplifiers are commonly seen installed in a cascode configuration, which improves the frequency response.
An ideal transconductance amplifier in a voltage follower configuration behaves at the output like a resistor of value 1/gm, between a buffered copy of the input voltage and the output. If the follower is loaded by a single capacitor C, the voltage follower transfer function has a single pole with time constant C/gm, [5] or equivalently it behaves as a 1st-order low-pass filter with a −3 dB bandwidth of gm/2πC.
An operational transconductance amplifier (OTA) is an integrated circuit which can function as a transconductance amplifier. These normally have an input to allow the transconductance to be controlled. [6]
A transresistance amplifier outputs a voltage proportional to its input current. The transresistance amplifier is often referred to as a transimpedance amplifier, especially by semiconductor manufacturers.
The term for a transresistance amplifier in network analysis is current controlled voltage source (CCVS).
A basic inverting transresistance amplifier can be built from an operational amplifier and a single resistor. Simply connect the resistor between the output and the inverting input of the operational amplifier and connect the non-inverting input to ground. The output voltage will then be proportional to the input current at the inverting input, decreasing with increasing input current and vice versa.
Specialist chip transresistance (transimpedance) amplifiers are widely used for amplifying the signal current from photo diodes at the receiving end of ultra high speed fibre optic links.
An operational amplifier is a DC-coupled electronic voltage amplifier with a differential input, a (usually) single-ended output, and an extremely high gain. Its name comes from its original use of performing mathematical operations in analog computers.
A negative-feedback amplifier is an electronic amplifier that subtracts a fraction of its output from its input, so that negative feedback opposes the original signal. The applied negative feedback can improve its performance and reduces sensitivity to parameter variations due to manufacturing or environment. Because of these advantages, many amplifiers and control systems use negative feedback.
In electronics, a common-base amplifier is one of three basic single-stage bipolar junction transistor (BJT) amplifier topologies, typically used as a current buffer or voltage amplifier.
A differential amplifier is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to the two inputs. It is an analog circuit with two inputs and and one output , in which the output is ideally proportional to the difference between the two voltages:
In electronics, a Schmitt trigger is a comparator circuit with hysteresis implemented by applying positive feedback to the noninverting input of a comparator or differential amplifier. It is an active circuit which converts an analog input signal to a digital output signal. The circuit is named a trigger because the output retains its value until the input changes sufficiently to trigger a change. In the non-inverting configuration, when the input is higher than a chosen threshold, the output is high. When the input is below a different (lower) chosen threshold the output is low, and when the input is between the two levels the output retains its value. This dual threshold action is called hysteresis and implies that the Schmitt trigger possesses memory and can act as a bistable multivibrator. There is a close relation between the two kinds of circuits: a Schmitt trigger can be converted into a latch and a latch can be converted into a Schmitt trigger.
In electronics, a common-emitter amplifier is one of three basic single-stage bipolar-junction-transistor (BJT) amplifier topologies, typically used as a voltage amplifier. It offers high current gain, medium input resistance and a high output resistance. The output of a common emitter amplifier is inverted; i.e. for a sine wave input signal, the output signal is 180 degrees out of phase with respect to the input.
A current mirror is a circuit designed to copy a current through one active device by controlling the current in another active device of a circuit, keeping the output current constant regardless of loading. The current being "copied" can be, and sometimes is, a varying signal current. Conceptually, an ideal current mirror is simply an ideal inverting current amplifier that reverses the current direction as well, or it could consist of a current-controlled current source (CCCS). The current mirror is used to provide bias currents and active loads to circuits. It can also be used to model a more realistic current source.
A Colpitts oscillator, invented in 1918 by Canadian-American engineer Edwin H. Colpitts using vacuum tubes, is one of a number of designs for LC oscillators, electronic oscillators that use a combination of inductors (L) and capacitors (C) to produce an oscillation at a certain frequency. The distinguishing feature of the Colpitts oscillator is that the feedback for the active device is taken from a voltage divider made of two capacitors in series across the inductor.
The asymptotic gain model is a representation of the gain of negative feedback amplifiers given by the asymptotic gain relation:
In electronics, a common-gate amplifier is one of three basic single-stage field-effect transistor (FET) amplifier topologies, typically used as a current buffer or voltage amplifier. In this circuit, the source terminal of the transistor serves as the input, the drain is the output, and the gate is connected to some DC biasing voltage, or "common," hence its name. The analogous bipolar junction transistor circuit is the common-base amplifier.
In electronics, a common-source amplifier is one of three basic single-stage field-effect transistor (FET) amplifier topologies, typically used as a voltage or transconductance amplifier. The easiest way to tell if a FET is common source, common drain, or common gate is to examine where the signal enters and leaves. The remaining terminal is what is known as "common". In this example, the signal enters the gate, and exits the drain. The only terminal remaining is the source. This is a common-source FET circuit. The analogous bipolar junction transistor circuit may be viewed as a transconductance amplifier or as a voltage amplifier.. As a transconductance amplifier, the input voltage is seen as modulating the current going to the load. As a voltage amplifier, input voltage modulates the current flowing through the FET, changing the voltage across the output resistance according to Ohm's law. However, the FET device's output resistance typically is not high enough for a reasonable transconductance amplifier, nor low enough for a decent voltage amplifier. As seen below in the formula, the voltage gain depends on the load resistance, so it cannot be applied to drive low-resistance devices, such as a speaker. Another major drawback is the amplifier's limited high-frequency response. Therefore, in practice the output often is routed through either a voltage follower, or a current follower, to obtain more favorable output and frequency characteristics. The CS–CG combination is called a cascode amplifier.
The cascode is a two-stage amplifier that consists of a common emitter stage feeding into a common base stage when using bipolar junction transistors (BJTs) or alternatively a common source stage feeding a common gate stage when using field-effect transistors (FETs).
This article illustrates some typical operational amplifier applications. A non-ideal operational amplifier's equivalent circuit has a finite input impedance, a non-zero output impedance, and a finite gain. A real op-amp has a number of non-ideal features as shown in the diagram, but here a simplified schematic notation is used, many details such as device selection and power supply connections are not shown. Operational amplifiers are optimised for use with negative feedback, and this article discusses only negative-feedback applications. When positive feedback is required, a comparator is usually more appropriate. See Comparator applications for further information.
Channel length modulation (CLM) is an effect in field effect transistors, a shortening of the length of the inverted channel region with increase in drain bias for large drain biases. The result of CLM is an increase in current with drain bias and a reduction of output resistance. It is one of several short-channel effects in MOSFET scaling. It also causes distortion in JFET amplifiers.
A Wilson current mirror is a three-terminal circuit that accepts an input current at the input terminal and provides a "mirrored" current source or sink output at the output terminal. The mirrored current is a precise copy of the input current.
The operational transconductance amplifier (OTA) is an amplifier that outputs a current proportional to its input voltage. Thus, it is a voltage controlled current source (VCCS). Three types of OTAs are single-input single-output, differential-input single-output, and differential-input differential-output, however this article focuses on differential-input single-output. There may be an additional input for a current to control the amplifier's transconductance.
The Miller theorem refers to the process of creating equivalent circuits. It asserts that a floating impedance element, supplied by two voltage sources connected in series, may be split into two grounded elements with corresponding impedances. There is also a dual Miller theorem with regards to impedance supplied by two current sources connected in parallel. The two versions are based on the two Kirchhoff's circuit laws.
In electronics, a transimpedance amplifier (TIA) is a current to voltage converter, almost exclusively implemented with one or more operational amplifiers. The TIA can be used to amplify the current output of Geiger–Müller tubes, photo multiplier tubes, accelerometers, photo detectors and other types of sensors to a usable voltage. Current to voltage converters are used with sensors that have a current response that is more linear than the voltage response. This is the case with photodiodes where it is not uncommon for the current response to have better than 1% nonlinearity over a wide range of light input. The transimpedance amplifier presents a low impedance to the photodiode and isolates it from the output voltage of the operational amplifier. In its simplest form a transimpedance amplifier has just a large valued feedback resistor, Rf. The gain of the amplifier is set by this resistor and because the amplifier is in an inverting configuration, has a value of -Rf. There are several different configurations of transimpedance amplifiers, each suited to a particular application. The one factor they all have in common is the requirement to convert the low-level current of a sensor to a voltage. The gain, bandwidth, as well as current and voltage offsets change with different types of sensors, requiring different configurations of transimpedance amplifiers.
In the theory of electrical networks, a dependent source is a voltage source or a current source whose value depends on a voltage or current elsewhere in the network.
A double-tuned amplifier is a tuned amplifier with transformer coupling between the amplifier stages in which the inductances of both the primary and secondary windings are tuned separately with a capacitor across each. The scheme results in a wider bandwidth and steeper skirts than a single tuned circuit would achieve.
