Transcript linear circuit analysis

LINEAR CIRCUIT
ANALYSIS
EE-111
ENGR. IMRAN AZIZ
Chapter 5: Transformers and Amplifiers
• Dependent Sources
• Circuit Analysis with Dependent Sources
• The Ideal Transformer
• Amplifiers
Introduction:
• Both amplifiers and transformers are examples of two-port
• A hi-fi system is more sophisticated two-port which takes weak
input signal and provides amplified output
• Both input and output port exhibit individual i-v characteristics
• Distinguishing feature of two port is relationship between input
and output signals, called the transfer characteristics.
• This inter-dependence between the ports is modeled with the
help of dependent sources.
5.1 Dependent Sources:
• Dependent sources are indispensable ingredient in modeling of
transformer and amplifier
• A dependent source acts much like an independent source
except that its voltage/current is being controlled by some other
voltage/current in the circuit.
• This can also release or absorb power
• Resistance Transformation:
• A dependent source is unable to initiate any voltage/current in a circuit; an
independent source is required to do that.
• Then what is the role of Dependent Source?
• Dependent source can be regarded as a generalized concept of resistance
• Resistance imposes constraint between voltage and current of same
branch
• Dependent source impose constraint between different branches
• This is the reason we’ll often get quite unexpected results based on our
experience of independent sources.
• We’ll understand it through an example:
• We wish to find the Req of below circuit:
• The dependent source monitors port voltage
vx being fed from left and drives the right side
by multiplying it with k.
• Here we can’t suppress the source, because
suppressing the source would mean to make k = 0 (short circuit)
• Proper way is to add the test voltage source at open terminals
• Then Req = v / i
• By Ohm’s Law:
• So, Req can have variety of different values depending upon k.
• Req can have infinite or even negative values due to the
presence of dependent source in the circuit, which indirectly
affects the voltage across R.
• The role of dependent source can be more appreciated by taking
some specific element values; let v = 1V and R = 1 Ohm.
• Now we’ll examine circuit behavior for different values of k.
• k = 0: Short circuit. i = 1 A, Req = R
• 0< k < 1: increasing value of k in given range,
increases the Req of the circuit.
• k < 0 : decreasing k below zero, makes Req approach to
zero.
• k > 1: Negative resistance behavior.
Positive resistance: test source is delivering power
Negative resistance: test source is receiving power
• Transistor Modelling:
• An important application of dependent source is transistor modeling.
• Current Gain (Beta) = Ic / IB.
• IE = IC + IB.
• IC is constant in the circuit regardless of the
value of VCE.
• Circuit symbol and model of npn BJT
• In circuits, having transistors, we can simply
replace it with its model and use the circuit
analysis techniques to calculate the desired
values.
• Voltage Divider Circuit:
• These equations are repeatedly
used when dealing with transistors.
5.2 Circuit Analysis with Dependent Sources
• We’ll use the same techniques of circuit analysis as before.
• A few things shall be taken care of:
• In general, values of controlling signals i.e ix and vx are not known but are
found by calculations of different equations
• Dependent sources can’t be suppressed to find Req; this would invalidate
constraint between controlled source and controlling signal.
• However, independent sources can be suppressed to find Req because
their values are independent of rest of circuitry.
• Thevenin’s and Nortan’s Equivalent:
• Nodal / Loop analysis can be used to find the Thevenin’s or Norton’s
Equivalent of one-port with dependent sources (Method 1):
• Generally open circuit values of vx / ix shall be different from short circuit
values.
• Method 2 can also be used to find Req by suppressing all the
independent sources and applying a test voltage in circuit. Then
Where v is voltage of test source.
• Source transformation techniques are also applicable in circuits with
dependent sources but we should avoid tempering controlling signals.
• Concluding Remarks:
• When looking for Thevenin’s / Norton’s Equivalents, its good practice to
pause and try developing a strategy to minimize the computational effort
• Try to analyze that which method is easier for specific circuit.
• When looking for Req, if voc and isc are zero, then we’ve to move towards
Method 2.
• If there is no independent source in circuit; obviously voc and isc are zero, then
we also have to move towards Method 2.
5.3 The Ideal Transformer
• Transformer is our first example of two port device.
• Two coils, called primary and secondary, are wound around
magnetic core
• Primary coil plays role of i/p port while secondary of o/p port
• N1 and N2 are no. of turns in windings, then, the turn ratio of
transformer is
• The function of dots is to identify signal polarities.
• If v1 and v2 are chosen to be positive at dotted terminal, then
they are in phase, otherwise, they are out of phase.
• Likewise, currents are in phase if one enters in dotted terminal
and other leaves the dotted terminal.
• Dots can be omitted when phase relationship is unimportant.
• Ideally transformer dissipates no energy. i.e power absorbed via
primary equals the power released by secondary.
• n > 1:Output voltage is greater than input voltage.
• n < 1:Output voltage is less than input voltage
• n = 1:Provides electrical isolation and suppress dc component.
• Circuit Model of Ideal Transformer:
• As v2 depends upon v1 and n, regardless of load, so secondary can
be modeled as dependent voltage source of value nv1.
• Likewise, i1 depends upon load and n, regardless of v1, so primary
can be modeled as dependent current source of value ni2.
THE END