Circuit Components

Properties of Circuit Components:

Linear Versus Nonlinear:

To behave linearly is to uphold the law of superposition.

Avoiding extreme situations many elements either have:

1) a range (or ranges) over which their defining variables(voltage, current) exhibit linear behavior, or

2) over even the smallest of defined ranges the elementsdefining variables behave in a non-linear way.

Time-Invariant versus Time-Variant:

Time-invariant if within analysis time framethe element remains constant

Time-variant if within analysis time frame the element is changing.

Circuit Components Properties of Circuit Components:

Lumped versus Distributed:

A component must be considered as distributed when the physical dimensions of an element become significant with respect to the propagation time of a signal across the element

A component can be considered as lumped when the physical dimensions of the component are of little significance.

Assuming lumped components avoids partial differential equations and greatly simplifies analysis and is valid for most circuit elements over a wide frequency range

Active versus Passive:

An active component supplies energy by converting one form of energy to another (eg. battery, transducer or transistor)

A passive component either only absorbs energy (eg. resistor, diode) or absorbs energy then later releases it (eg. capacitor or inductor)

Properties of Circuit Components:

Independent Power Sources:

Independent Voltage Sources:

- most common power source is the voltage source.

- ideally maintains a constant voltage across its terminalsindependent of the amount of current it supplies

- ideally has zero internal resistance (impedance).

- practical voltage sources are modeled as an ideal voltage sourcein series with some small but non-zero internal resistance.

- batteries, generators and photovoltaic cells perform work on charge carriers.

- energy transfer processes must be at least in principle reversible .

Properties of Circuit Components:

Independent Voltage Sources:

- amount of work done per unit charge is:

V = dW

dq( Joules

Coulomb or V)

-V is not actually a forcebut rather has units of energy per charge.

- work done by the conversion of some other energy source(chemical, kinetic) into electric potential energy

- electric energy is then stored in the electric and magnetic fields of thecircuit components (capacitors, inductors)or converted to thermal energy by the resistors in the circuit.

Properties of Circuit Components:

Independent Voltage Sources:

Properties of Circuit Components:

Independent Current Sources:

- not as common as voltage sources but are veryimportant both theoretically and in semiconductorcircuits.

- ideal current source maintains a constant output current,regardless of the voltage across its terminals.

- infinite internal resistance (impedance).

- practical current sources are modeled as an ideal current source inparallel with some large but finite internal resistance (impedance).

Properties of Circuit Components:

Independent Current Sources:

Properties of Circuit Components:

Dependent Power Sources:

- output voltage or current is dependent or controlled bysome other voltage or current in the circuit

- arise from complex physical interactions in electronic devices

- e.g. base current controls collector current in a bipolar junctiontransistor

Voltage Controlled Voltage Source (VCVS):

- vi is independent control voltage acrosssome specified circuit element(s)

- A represents the voltage gain(dimensionless)

Current Controlled Voltage Source (ICVS):

- ii is independent control current throughsome specified circuit element(s)

- Rm is termed the transresistance (ohms)

Properties of Circuit Components:

Voltage Controlled Current Source (VCIS):

- vi independent control voltage acrosssome specified circuit element(s)

- gm is termed the transconductance(siemans)

Current controlled Current Source: (ICIS)

- ii independent control currentthrough some circuit element(s)

- represents the current gain(dimensionless)

Dependent Power Sources:

Properties of Circuit Components:

Resistor:

- linear, lumped, time invariant element of specific geometry and material composition to constitute a specified amount of ohmic resistance

R = V / I

Capacitor:

- linear, lumped, time invariant element of specific geometry and material composition to constitute a

specified amount of capacitance

C = q / V

Properties of Circuit Components:

Passive Components:

Inductor:

- linear, lumped, time invariant element of specific geometry and material composition to constitute a

specified amount of inductance

L = L / I

Diodes:

- nonlinear, lumped, time invariant semi-conductor device with specific voltage current relationship

Properties of Circuit Components:

Circuit Parameters of Interest:

- current and voltage

- want as functions of time or frequency for various types of power sources (driving functions)

Modes of Excitation (Driving Functions):

- DC - direct voltage or current supplies

- AC - value of applied voltage or current changes in some specified pattern (eg. sine or square wave excitation)

- initial conditions (transient response only)

Properties of Circuit Components: