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Cheat sheet for Circuit Analysis I | E E 210, Study notes of Electrical and Electronics Engineering

Cheat sheet Material Type: Notes; Professor: Lee; Class: CIRCUIT ANALYSIS I; Subject: Electrical Engineering; University: San Diego State University;

Typology: Study notes

2011/2012

Uploaded on 02/01/2012

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EE210 Cheat Sheet
Basic Definitions:
NOTE: current only changes when there are 3
or more devices connect to the same two
nodes
NOTE: Voltage only changes when passing
through a device
Basic Definition:
Circuit: An interconnection of electrical devices(net
work of devices
Device: Components in the circuit (D) (5)
Loop: Starts at a terminal and transverse around
branches of a circuit ending at the same terminal (3)
Mesh: A special loop that doesn’t have any loops inside
of it. (2)
Node: A point on the circuit where 2 or more devices
have a common connection (4)
Ground: Reference node (1-node 4)
Circuit:
Linear Devices:
Homogeneity:
Superposition:
Kirchhoff’s Laws:
Voltage law (KVL): (applies to loops)
Current law (KCL): (applies to nodes)
Independent Sources:
Independent Voltage Sources
a)constant or time varying voltage
b)constant voltage
D1
Node 1
Loop 2
Mesh 1
Loop 1
Loop 3
Mesh 2
Branch
es
Node 2
Node 3
Node 4 aka
reference node
pf3
pf4
pf5
pf8
pf9
pfa

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EE210 Cheat Sheet Basic Definitions:

NOTE: current only changes when there are 3 or more devices connect to the same two nodes

NOTE: Voltage only changes when passing through a device

Basic Definition: Circuit: An interconnection of electrical devices(net work of devices Device: Components in the circuit (D) (5) Loop: Starts at a terminal and transverse around branches of a circuit ending at the same terminal (3) Mesh: A special loop that doesn’t have any loops inside of it. (2) Node: A point on the circuit where 2 or more devices have a common connection (4) Ground: Reference node (1-node 4)

Circuit:

Linear Devices: Homogeneity: Superposition:

Kirchhoff’s Laws: Voltage law (KVL): (applies to loops) Current law (KCL): (applies to nodes)

Independent Sources: Independent Voltage Sources

a)constant or time varying voltage b)constant voltage

D

D

D

D

D

Node 1

Loop 2

Mesh 1

Loop 1 Loop 3

Mesh 2

Branch es

Node 2

Node 3

Node 4 aka reference node

Independent Current Source

Dependent Sources: Current Controlled Voltage Source Voltage Controlled Voltage Source

Current Controlled Current Source Voltage Controlled Current Source

Ohm’s Law(resistors):

Resistors: Passive device that absorbs power NOTE: ONLY VOLTAGE CHANGE

Resistors in Series: Resistance: Conductance:

Voltage Division Rule: (in series)

Resistors in Parallel: Resistance: Conductance:

Current Division Rule: (in parallel)

Thevenin’s Theorem A linear two terminal circuit can be replaced by an equivalent circuit consisting of a voltage source in series with a resistor where is the open circuit voltage at the terminals and is the equivalent resistance at the terminals when the independent sources are turned off.

Find and

  1. Remove the load
  2. Find open circuit with all sources in place and call it
  3. Find across all terminals.

NOTE: If it has all independent sources zero all sources to find by finding equivalent resistor. NOTE: If it has dependent sources zero all independent sources and apply either a test voltage or test current and

find or respectively.

NOTE: For independent current sources you open the circuit

For independent voltage sources you short circuit

Norton’s Theorem: A linear two terminal circuit can be replaced by an equivalent circuit consisting of a current source in parallel with a resistor , where is the short circuit current through the terminals and is the equivalent resistance at the terminals when the independent sources are turned off.

Find

  1. Remove the load
  2. Find short circuit with all sources in place and call it.
  3. Find across all terminals.

NOTE: If it has all independent sources zero all sources to find by finding equivalent resistor. NOTE: If it has dependent sources zero all independent sources and apply either a test voltage or test current and

find or respectively.

NOTE: For independent current sources you open the circuit

For independent voltage sources you short circuit

Maximum Power:

Capacitors:

No instantaneous change in voltage. Open circuit when there is a constant voltage across the terminals. ALWAYS Positive to Negative Polarity Voltage: Current: Power: Energy:

RC and RL Circuit:

  1. Find the steady state response of the capacitor or inductor at the initial time.
  2. Find the voltage or current of the capacitor or inductor respectively just as the time changed happened.
  3. Find the steady state response of the capacitor or inductor after the change. NOTE: to find the value find the Thevenin’s and/or Norton’s Equivalent circuit of the device of the known.
  4. Plug the values of either current or voltage into the general equation below:
  5. For capacitors: for inductors NOTE: The used for is either the Resistance of the Norton’s or Thevenin’s equivalent on device being found. Singularity Functions:
  6. For (the unit step function) the relationship is shown below:

Therefore when then the relationship of the unit step function is shown below:

Therefore when then the relationship of the unit step function is shown below:

  1. Looking at the voltage/current pulse graph the sign in front of the terms is determined to be for terms or for terms.
  2. The magnitude of the is dependent on the amount increased/decreased and is placed in front of the terms shown below:
  3. When expressing the pulse function of voltage or current start from the left and end at the right of the graph. If there is a ramp then it is designated as r where it follows the same rules as the in step 1.
  4. Then calculate the slope of the ramp. If the slope is positive then r is added by the magnitude of the slope if the slope is negative then r is subtracted by the magnitude of the slope.

Special Cases: If the slope suddenly stops and becomes a horizontal line then a of equal and opposite slope is added.

If the slope is decreasing by a negative value of the same slope, then a of twice the opposite of the slope is added.

Step Responses of RC/RL Circuit:

  1. Set the voltage or current of the source to 1. This is representative of.
  2. Find the steady state response of the capacitor or inductor at the specified time to find initial condition.
  3. Find the voltage or current of the capacitor or inductor respectively just as the changed happened.
  4. Find the steady state response of the capacitor or inductor after the change. NOTE: to find the value find the Thevenin’s and/or Norton’s Equivalent circuit of the device.
  5. Plug the values of either current or voltage into the general equation below for the active response: or
  6. For capacitors: for inductors NOTE: The used for is either the Resistance of the Norton’s or Thevenin’s equivalent on device being found.
  7. Now replace add the step response into the equation.

NOTE:

When finding more than just the voltage or current of capacitor or inductor e.g. resistor on the circuit, need to look at the device you first solving for. 1 st^ Solving For 2 nd^ Solving For General Form Differentiation Term Capacitor Resistor Voltage

Capacitor Resistor Current

Inductor Resistor Voltage

Inductor Resistor Current

Sinusoidal Voltage:

Where is the amplitude, is the angular frequency For a typical cycle the period is :

Frequency:

Therefore:

The general expression for a sinusoidal voltage is: where is the phase

Sinusoid-Phasor Tranformation Time Domain Phasor Domain

Voltage-Current Relationships:

Element Time Domain Frequency Domain

Impedance/Admittance:

and

This can be expressed in rectangular or polar form.

Where:

and

And and Element Impedance Admittance

Impedance Combinations: In series:

Voltage Divider Rule:

In parallel:

also same as

Current Divider Rule:

Operational Amplifiers (Op-Amp):

Non-Ideal Op-Amp

Typical ranges for op amp parameters Parameter Typical Range Ideal values Open-loop gain, to Input resistance, to Output resistance, to Supply voltage, to

Ideal Op-Amp

  1. Infinite open-loop gain
  2. Infinite input resistance
  3. Zero output resistance, Characteristics:
  4. Currents into both input terminals are zero. ,
  5. The voltages at the two branches entering the op amp are equal.

SPECIAL CASES:

Inverting Op-Amps: Noninverting input is grounded and is connected to inverting input through