Things you should know
E72 takes off where E11 left off. Because of this, there is certain knowledge from E11 that will be assumed. You don't have to be able to easily apply all the various methods of solution that you used in those courses -- the ones that are important will come back to you as you use them. There are, however, some fundamental things that you should know.
The rest of this indroduction is devoted to a re-statement and review of the salient material from E11. Look it over to see if there are any topics with which you feel uncomfortable. If there are any, you may want to break out your E11 (and/or E12) book and review. Again - you don't need to be facile with all the fine points, but you should feel at ease with each topic.
The preview is broken up into four parts:
Passive Linear Circuit Elements
high frequency - acts as short circuit
low frequency - open circuit
high frequency - open circuit
low frequency - short circuit
|Time Constant (with Resistor)||.||τ=RC||τ=L/R|
Voltage and Current Sources
|Independent DC voltage source||Output voltage is constant (at any current)|
|Independent AC voltage source||Output voltage varies sinusoidally.|
|Current Source||Output current is constant (at any voltage).|
|Voltage dependent voltage source
|Output voltage is proportional to a control voltage, Vc (with proportionality constant Av -- Av is unitless)|
|Current dependent current source
|Output current is proportional to a control current, Ic (with proportionality constant Ai -- Ai is unitless)|
|Current dependent voltage source
Output voltage is proportional to a control current, Ic (with proportionality constant Rm -- Rm has units of ohms)
|Voltage dependent current source (Transconductance Amplifier)||Output current is proportional to a control voltage, Vc (with proportionality constant Gm -- Gm has units of Siemens (Conductivity))|
Circuit Analysis MethodsThere are certain circuit analysis methods which you must know to successfully complete the work of this course. The major topics include:
v1-v2-v3-v4=0, or v1=v2+v3+v4
As an example, consider the circuit below:
We can find the voltage across the 1kΩ resistor by consisdering the voltage source and the current source independently.
Consider Voltage Source Alone
(Current Source set to zero -- an open circuit)
Consider Current Source Alone
(Voltage Source set to zero -- a short circuit)
Voltage = 1.333 volts (by voltage divider)
(333Ω=1k in parallel with 500 -- 333=1k||500)
Voltage = 0.333 volts (by Ohm's law)
Therefore, the total voltage (by superposition)=0.333+1.333=1.666 volts.
When applying the Thevenin Theorem there are three cases.
- Case 1: Only independent sources - the typical case. In the typical case, there are no dependent sources in the circuit to be Thevenized. To find the Thevenin equivalent, first find the open circuit voltage, Voc, this is the Thevenin voltage. To find the Thevenin resistance, set all sources to zero and find the resistance of the resulting circuit
Consider again the circuit from above,
and try to find the Thevenin circuit at the terminals (i.e., across the 1k resistor). From the discussion of superposition, we know the open circuit voltage, Voc, is 1.666 volts. The Thevenin resistance, RT, is found by finding the equivalent resistance of the circuit with all source set to zero, as shown below
Obviously the Thevenin resistance, RT, is 1k||500=333Ω. Therefore the resulting circuit is:
- Case 2: Independent and Dependent Sources. If the circuit to be Thevenized has both dependent and independent source, the method described above cannot be used to find the Thevenin resistance. Instead, you must find the short circuit current, Isc (current through short circuit at terminals). Then the Thevenin resistance is given by RT=Voc/Isc.
- Case 3: Only Dependent Sources. If only dependent sources are present, then the Thevenin voltage is zero, and the Thevenin resistance is determine by applying a test voltage Vtest and the terminals and determining the resulting current, Itest. The Thevenin resistance is given by RT=Vtest/Itest. (Likewise, for this third case, you can apply a test current and measure the resulting voltage).
On to System Behavior
On to Problems
Comments or Questions?