Small signal model
Encyclopedia
Small-signal modeling is a common analysis technique in electrical engineering
which is used to approximate the behavior of nonlinear device
s with linear equations. This linearization is formed about the DC
bias point of the device (that is, the voltage
/current
levels present when no signal is applied), and can be accurate for small excursions about this point.
circuits, generally carry small time-varying signals on top of a constant bias. This suggests using a method akin to approximation by finite difference method to analyze relatively small perturbations about the bias point.
Any nonlinear device which can be described quantitatively using a formula can then be 'linearized' about a bias point by taking partial derivatives of the formula with respect to all governing variables. These partial derivatives can be associated with physical quantities (such as capacitance
, resistance
and inductance
), and a circuit diagram relating them can be formulated.
Small-signal models exist for electron tube
s, diode
s, field-effect transistor
s (FET) and bipolar transistors
, notably the hybrid-pi model
and various two-port network
s.
, capacitance and resistance of the diode. This procedure is described in more detail under diode modeling, which provides an example of the linearization procedure followed in all small-signal models of semiconductor devices.
A large signal model on the other hand takes into account the fact that the large signal actually affects the operating point and takes into account that elements are non-linear and that circuits can be limited by power supply values. A small signal model ignores supply values.
Electrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...
which is used to approximate the behavior of nonlinear device
Nonlinear device
In an electric circuit, a nonlinear element or nonlinear device is an electrical element which does not have a linear relationship between current and voltage. A diode is a simple example...
s with linear equations. This linearization is formed about the DC
Direct current
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...
bias point of the device (that is, the voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
/current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
levels present when no signal is applied), and can be accurate for small excursions about this point.
Motivation
Many electronic circuits, such as radio receivers, communications, and signal processingSignal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
circuits, generally carry small time-varying signals on top of a constant bias. This suggests using a method akin to approximation by finite difference method to analyze relatively small perturbations about the bias point.
Any nonlinear device which can be described quantitatively using a formula can then be 'linearized' about a bias point by taking partial derivatives of the formula with respect to all governing variables. These partial derivatives can be associated with physical quantities (such as capacitance
Capacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
, resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
and inductance
Inductance
In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...
), and a circuit diagram relating them can be formulated.
Small-signal models exist for electron tube
Electron tube
Electron tube can be used to describe either of two things:* Vacuum tube* Gas-filled tube...
s, diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...
s, field-effect transistor
Field-effect transistor
The field-effect transistor is a transistor that relies on an electric field to control the shape and hence the conductivity of a channel of one type of charge carrier in a semiconductor material. FETs are sometimes called unipolar transistors to contrast their single-carrier-type operation with...
s (FET) and bipolar transistors
Bipolar junction transistor
|- align = "center"| || PNP|- align = "center"| || NPNA bipolar transistor is a three-terminal electronic device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons...
, notably the hybrid-pi model
Hybrid-pi model
The hybrid-pi model is a popular circuit model used for analyzing the small signal behavior of bipolar junction and field effect transistors. The model can be quite accurate for low-frequency circuits and can easily be adapted for higher frequency circuits with the addition of appropriate...
and various two-port network
Two-port network
A two-port network is an electrical circuit or device with two pairs of terminals connected together internally by an electrical network...
s.
Variable notation
- Large-signal DC quantities are denoted by uppercase letters with uppercase subscripts. For example, the DC input bias voltage of a transistor would be denoted
.
- Small-signal quantities are denoted using lowercase letters with lowercase subscripts. For example, the input signal of a transistor would be denoted as
.
- Total quantities, combining both small-signal and large-signal quantities, are denoted using lower case letters and uppercase subscripts. For example, the total input voltage to the aforementioned transistor would be
.
Example: PN junction diodes
The (large-signal) Shockley equation for a diode can be linearized about the bias point or quiescent point (sometimes called Q-point) to find the small-signal conductanceConductance
Conductance may refer to:* Electrical conductance, the ability for electricity to flow a certain path* Fluid conductance, the ability for fluid to transmit through materials* Thermal conductivity, the ability for temperatures to transmit through materials...
, capacitance and resistance of the diode. This procedure is described in more detail under diode modeling, which provides an example of the linearization procedure followed in all small-signal models of semiconductor devices.
Differences between Small Signal and Large Signal
A small signal model takes a circuit and based on an operating point (bias) it linearizes all the components. Nothing changes because the assumption is that the signal is so small that the operating point (gain, capacitance etc) doesn't change.A large signal model on the other hand takes into account the fact that the large signal actually affects the operating point and takes into account that elements are non-linear and that circuits can be limited by power supply values. A small signal model ignores supply values.
See also
- Diode modellingDiode modellingIn electronics, diode modelling refers to the mathematical models used to approximate the actual behavior of real diodes to enable calculations and circuit analysis. A diode's I-V curve is nonlinear...
- Hybrid-pi modelHybrid-pi modelThe hybrid-pi model is a popular circuit model used for analyzing the small signal behavior of bipolar junction and field effect transistors. The model can be quite accurate for low-frequency circuits and can easily be adapted for higher frequency circuits with the addition of appropriate...
- Early effectEarly EffectThe Early effect is the variation in the width of the base in a bipolar junction transistor due to a variation in the applied base-to-collector voltage, named after its discoverer James M. Early...
- SPICESPICESPICE is a general-purpose, open source analog electronic circuit simulator.It is a powerful program that is used in integrated circuit and board-level design to check the integrity of circuit designs and to predict circuit behavior.- Introduction :Unlike board-level designs composed of discrete...
- Simulation Program with Integrated Circuit Emphasis, a general purpose analog electronic circuit simulator capable of solving small signal models.