# Circuit Theory/One Port Devices

There are many circuits that can solve any particular task. Kirchhoff or
any other analysis technique can not describe the bare minimum, most
simple, alternative to an existing circuit that works.

The goal is to figure out a circuit\'s characteristics \... like an
eigenvalue \... the minimal parameters that
totally define it. The minimal characteristics or parameters serve two
purposes:

-   Enable design of alternative, cheaper, simpler circuits that do the
    same thing
-   Help designers using the existing circuit predict its impact on
    other circuits attached to it.

## One-Port

![](One_Port_Circuit.svg "One_Port_Circuit.svg")

Impedance, resistance and reactance are often drawn as a rectangle
instead of their normal circuit symbols. This is the beginning of
dealing with the real world rather than the ideal.

A \"port\" hides what is inside of it like a \"black
box\".

A resistor, capacitor, inductor and power source are one-port (two-wire)
devices. But in the real world a resistor could also have some
inductance, or capacitance, or act as an antenna channeling wireless
energy into the circuit.

More generally, a one-port circuit can have any number of passive
elements, independent and dependent sources and nodes. A port can be
described as a circuit that has been designed, analyzed and tested. At
this point, a circuit\'s internal details, its design, and its theory of
operation are no longer important. It becomes a building block. Complex
circuits may consist of a few ports where each port itself may be
complex.

When ports are named, miniaturized and mass-produced, they become a new
circuit device.

One-port devices are usually found at the beginning and the end of a
circuit. The middle of a circuit is built with two-port
devices, which are covered later.

A port has characteristics besides its impedance and whether it contains
a source or not. A port has parameters. The
ideal parameters we have been studying are sometimes called
lumped element parameters. These
parameters may change depending on how the port is \"driven\". Ports can
have different \"driving
points\".

## Example

Suppose we are going to connect a DC Voltage power supply to points a
and b. The goal is to characterize the insides of the box that contains
a DC voltage source and a couple of resistors. Do this by:

-   Plot V~ab~ as depending upon the current (instead of the actual
    situation where current is dependent upon the added voltage supply)
    so that the slope is resistance. From the plot find the slope
    (resistance). What does the vertical, V~ab~ axis intercept
    represent? What does the horizontal (current) axis intercept
    represent?
-   Calculate the V~ab~ if nothing is attached to the one port device.
-   Zero the voltage source and calculate the resistance between a and
    b.
-   Create another one port device that behaves the same with just one
    source and resistor. Simulate it and show that it produces the same
    V~ab~ curve or line.

<File:Example26aa.png%7CCircuit> that problem statement is referring to
<File:Example26c.png%7CSince> current is on the independent (x) axis and
voltage is dependent, need a current source.
<File:Example26e.png%7CSimulation> that can be found at
circuitlab.com

### Plot V~ab~

:   Circuit was simulated at
    circuitlab
    resulting in the plot above that matches the formula below.
:   Slope of the line is 66.66667 ohms and the intercept is -1 volt.
:   The equation of the line can be formed by node analysis at a:
    $$I - \frac{V_{ab}}{100} - \frac{V_{ab}+3}{200} = 0$$
:   Solving for V~ab~
    $$V_{ab} = \frac{200*I}{3} - 1$$
:   Can see in the simulation that the intercept when i = 0 is -1 and
    slope is 200/3.

### Calculate V~ab~ with nothing attached

Nothing attached means the current is zero, so from the equation
V~ab~=-1 \... which is the V~ab~ vertical axis intercept. !Circuit with
voltage source shorted so can compute resistance between points a and
b.

### Zero voltage source, calculate resistance between a and b

After shorting the voltage source, have 200 and 100 ohm resistors in
parallel so:

$$R_{ab} = \frac{1}{\frac{1}{200} + \frac{1}{100}} = \frac{200}{3}$$
which is the slope of the equation.

### Create simpler one port device

<File:Example26d.png%7Csimple> circuit the performs exactly the same way
as the more complicated one <File:Example26e.png%7Csimulation> at
circuitlab.com
is same as the 2 resistor circuit with -3 volt source

