In the lab, the open-circuit voltage measured across an
unknown circuit's terminals equals
.
When a 1Ω resistor is place across the terminals, avoltage of
appears.
What is the Thévenin equivalent circuit?
What voltage will appear if we place a 1F capacitor
across the terminals?
Mystery circuit
We want to determine as much as we can about the circuit lurking in the impenetrable box shown in
[link] .
A voltage source
V
has been attached to the left-hand terminals, leaving the right terminals for tests and measurements.
Sammy measures
V when a 1 Ω resistor is attached to the terminals.
Samantha says he is wrong.Who is correct and why?
When nothing is attached to the right-hand terminals, a voltage of
V is measured.
What circuit could produce this output?
When a current source is attached so that
amp, the voltage
is now 3 V.
What resistor circuit would be consistent with this and the previous part?
More circuit detective work
The left terminal pair of a two
terminal-pair circuit is attached to a testingcircuit. The test source
equals
(
[link] ).
We make the following measurements.
With nothing attached to the terminals on the
right, the voltage
equals
.
When a wire is placed across the terminals on
the right, the current
was
.
What is the impedance “seen” from the terminals
on the right?
Find the voltage
if a current source is attached to the
terminals on the right so that
.
Linear, time-invariant systems
For a system to be completely characterized by atransfer function, it needs not only be linear, but also
to be time-invariant. A system is said to betime-invariant if delaying the input delays the output
by the same amount. Mathematically, if
,
meaning
is the output of a system
when
is the input,
is the time-invariant if
for all delays
and all inputs
.
Note that both linear and nonlinear systems have thisproperty. For example, a system that squares its input
is time-invariant.
Show that if a circuit has fixed circuit elements
(their values don't change over time), itsinput-output relationship is time-invariant.
Hint : Consider the differential
equation that describes a circuit's input-outputrelationship. What is its general form? Examine the
derivative(s) of delayed signals.
Show that impedances cannot characterize
time-varying circuit elements (R, L, and C).Consequently, show that linear, time-varying systems
do not have a transfer function.
Determine the linearity and time-invariance of the
following. Find the transfer function of the linear,time-invariant (LTI) one(s).
diode
Long and sleepless nights
Sammy went to lab after a long, sleepless night, and
constructed the circuit shown in
[link] .
He cannot remember what the circuit, represented by theimpedance
, was. Clearly,
this forgotten circuit is important as the output is thecurrent passing through it.
What is the Thévenin equivalent circuit seen by
the impedance?
In searching his notes, Sammy finds that the circuitis to realize the transfer function
Find the impedance
as well as values for the other circuit elements.
Questions & Answers
Biology is a branch of Natural science which deals/About living Organism.
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things