Engineering Circuit Analysis
(V0) = (A0)*((IN+)-(IN-)) explain this equation
1. (IN+) is the noninverting input voltage - in the picture, Pins 3, 6, 9, 12 are the noninverting input 2. (IN-) is the inverting input voltage - in the picture, Pins 2, 5, 10, 13 are the inverting input 3. all voltages are measured with respect to ground 4. (A0) is the gain of the op-amp
What is procedure to determine op-amp circuits using the linear models
1. Identify Op Amp nodes 2. Redraw the circuit cutting out the Op Amp 3. Draw components of linear OpAmp 4. Redraw circuit if it needed
how many cases are in the norton and Thevenin technique?
1. Independent circuit 2. Independent and dependent circuit 3. dependent circuit
What are the main thing in the linear model of op amp?
1. Input resistance- Ri 2. Output resistance - Ro 3. Gain - Ao
There are 3 ways to solve KCL
1. Matlab 2. Gaussian elimination 3. Matrix analysis
What are equivalent circuit forms
1. Series resistors will be added 2. Parallel resistors will be multiplication of them will be divided by their sum 3. Series voltage will be added if they are in the same direction 4. Parallel current will be subtract if they are same direction
If there are other branches without no current source then
1. The path for this loop current can be obtained by open - circuiting the current souce Fig. 3.24c. 2. Think that open - circuiting is connected to mesh current, then add both of them. Another word think it as one loop current. Fig. 3.24d
Rule for circuits containing dependent source
1. Treat them like independent source 2. Write controlling equation for the dependent source.
Circuit and model for unity gain buffer
1. Write KVL law for Vs node 2. Write KVL law for Vo node 3. Write controlling value equation 3. Then Vo / Vs
what are the requirement of linearity ?
1. additivity 2. Homogeneity
How many ways power supplies affect om-amp performance ?
1. each op-amp has minimum and maximum supply ranges over which the op-amp is guaranteed to function 2. for proper operation, the input and output voltages are limited to no more than the supply voltages
How to use linearity and assumption to find values ?
1. use given value to find the main thing. 2. then use this value and find original value
conditions of the general solution of the first order equation
1. x(∞) = K_1 2. x(0) = K_1 + K_2
A dc current in the conductor main point
A dc current does not vary with time, so the voltage across the inductor is zero. So inductor is short circuit to dc
What is mesh ?
A mesh is a special kind of loop that does not contain any loops within it.
what is short circuit ?
A short circuit (sometimes abbreviated to short or s/c) is an electrical circuit that allows a current to travel along an unintended path with no or very low electrical impedance. This results in an excessive current flowing through the circuit. The opposite of a short circuit is an "open circuit", which is an infinite resistance between two nodes.
What are (Vcc) and (Vee) ?
Amplification requires power that is provided by the dc voltage sources connected to pins. In the picture, those are pin 4, 11
what is an inductor ?
An inductor is a circuit element that consists of a conducting wire usually in the form of a coil.
What is equation for finding the number of linear independent equation for loop analysis
B - N + 1 B is branch N is node
what is the capacitance of two parallel plates respect to A and distance d?
C = epcilon0 * A / d
Nodal Analysis
Choose one node as the reference node, and all the other node voltages are defined with respect to that node. This node also called ground because it has zero potential
How does current flow with respect to Voltage?
Current will flow from the node of higher potential to the node of lower potential.
What is the unit of capacitance?
Farad, Capacitance is measured in coulumbs per volt or farads
What is the ideal op-amp model and condition ?
First condition :Ro = 0, Ri = infinity , Ro = zero Second condition : i+ = i- = 0, v+ = v- The ground terminal shown on the op-amp is necessary for signal current return, and it guarantees that Kirchhoff's current law is satisfied at both the op-amp and the ground node in the circuit.
What is op-amp ?
Good voltage amplifier. In other words, the output voltage is a scaled replica of the input voltage
Nodal Analysis's omh's law
I = (Vm - Vn) / R Vm and Vn has to be measured with respect to the same point, that is ground. All the nonreference nodes are measured with respect to only one reference node.
What is cons of planar circuit?
If circuit is planar, the loops are more easily identified
Matrix Analysis equation
If general form of equation, GV = I Then , solution will be V = (G^-1)I
If there is R in the middle of two current
If, both current have same direction i1 - i2 Else, i1 + i2
What is super position?
In any linear circuit containing multiple independent sources, the current or voltage at any point in the network may be calculated as the algebraic sum of the individual contributions of the each source acting alone. and any remaining voltage sources are made by zero by replacing them with short circuits( V = 0), and any remaining current sources are made zero by replacing them with open circuits.
What is inspection KCL?
In general, if KCL is applied to node j with node voltage v_j , the coefficient of v_j is the sum of all the conductances connected to node j and the coefficients of the other node voltages (e.g., v_j−1, v_j+1) are the negative of the sum of the conductances connected directly between these nodes and node j. The right-hand side of the equation is equal to the sum of the currents entering the node via current sources. Therefore, the left-hand side of the equation represents the sum of the currents leaving node j and the right-hand side of the equation represents the currents entering node j.
what is main role of capacitor ?
In the ideal case, the capacitor will hold the charge for an indefinite period of time, if the source is removed. If at some later time an energy-absorbing device (e.g., a flash bulb) is connected across the capacitor, a discharge current will flow from the capacitor and, therefore, the capacitor will supply its stored energy to the device.
What is symbol of inductance ?
L and unit is henry
How many linearly independent equation do we need to solve KCL completely?
N - 1 equation.
What is planar circuit?
No conductor cross another conductor
how are charge transferred ?
Positive charges will be transferred to one plate and negative charges to the other.
What is single supply ?
Receive only one voltage which is Vcc and Vee is connected to ground .
Kirchhoff's Current Law
States that all of the current entering a circuit branch must exit again and the algebraic sum of the currents entering any node is zero
Kirchhoff's Voltage Law
States that the algebraic sum of the voltages around any loop is zero.
the power to the inductor expression
The power delivered to the inductor can be used to derive the energy stored in the element.
in order to find solution of the differential equation, what method do we should use ?
The state variable approach, we will write the equation for the voltage across the capacitor or the equation for the current across through the inductor
What is buffer amplifier ?
The voltage follower acts as buffer amlifier. THE VOLTAGE FOLLOWER ISOLATES ONE CIRCUIT FROM ANOTHER ESPECIALLY USEFUL IF THE SOURCE HAS VERY LITTLE POWER
If circuit contain dependent source
Then symmetrical condition will not work.
A network that depicts an op-amp
Using voltage division at the input and again at the output, we have this formula Vo/Vs = [Ri/(Ri+Rth1)]*Ao*[(RL)/((Ro)+(RL))]
Ohm's Law
V=IR, GV = I, where G is inductance
What is dual supply ?
Vcc and Vee are connected to reference node by serial. And receive 2 voltages plus and minus
the consequence of changing magnetic field.
a changing magnetic field produced a voltage that was proportional to the time rate of change of the current that produced the magnetic field
What is saturation region ?
an increase in the input voltage may not yield a corresponding increase in the output voltage
in the second order case
an inductor and a capacitor are present simultaneously
what is the continuity of current ?
an inductor tells us that the current flowing through an inductor just after a switch moves is the same as the current flowing through an inductor just before that switch moves.
what do we say about capacitor in dc ?
capacitor in dc is an open circuit to dc. And current flowing through the capacitor is zero. I = 0.
What is the supernode ?
choose 2 nonreference node in the circuit with respect to reference node. And combine it as one
if the circuit has a small time constant, then what will happen?
circuit settles down quickly to a steady-state value
Norton equivalent circuit
i = - Vo/ Rth + Isc
what is constant capacitance equation ?
i = C*dv / dt
how does energy stored in the electric field discharge ?
if a circuit is somehow connected across the capacitor that provides a path through which the negative charges move to the positive charges. The rate at which the energy is discharged is a direct function of the parameters in the circuit that is connected across the capacitor's plates.
What is rail-to-rail inputs and outputs?
if inputs/outputs can reach within a few dozen millivolts of the supplies
Why do a parallel connection of voltage sources and a series connection of current sources forbidden ?
if the sources are not pointing in the same direction and have exactly the same values
mesh equation inspection
if we assume all of the mesh currents to be in the same direction (clockwise or counterclockwise), then if KVL is applied to mesh j with mesh current ij , the coefficient of ij is the sum of the resistances in mesh j and the coefficients of the other mesh currents (e.g., ij−1, ij+1) are the negatives of the resistances common to these meshes and mesh j. The right-hand side of the equation is equal to the algebraic sum of the voltage sources in mesh j. These voltage sources have a positive sign if they aid the current flow ij and a negative sign if they oppose it.
why do we need time constant ?
it will tell us that how fast the circuit will respond to changes.
The value of nodal analysis
once we know nodal voltages we can calculate current, power absorbed or supplied by any element
what is equation of the charge on the capacitor is proportional to the voltage across it ?
q = Cv
Norton's Theorem
similar to thevenin's theorem, but the equivalent circuit is an independent current source in parallel with a resistor
Thevenin's Theorem
states that we can replace the entire network, exclusive of the load, by an equivalent circuit that contains only an independent voltage source in series with a resistor in such a way that the current-voltage relationship at the load is unchanged.
capacitors
store energy in their electric field(electrostatic energy)
inductors
store energy in their magnetic field
What is stray capacitance?
stray capacitance is present any time there is a difference in potential between two conducting materials separated by a dielectric.
The node equation for networks containing only resistors and independent current sources can be written in __.
symmetrical from
what will happen if one mesh have independent current source?
that mesh current will be equal to independent current source
what stores energy by electric field?
the charge differential between the plates creates an electric field that stores energy.
Current Division
the current i(t) from the source divides between the two branches is called current division v(t) = (Rp)*i(t) Rp is the sum of parallel resistor in single node pair circuit.
according to the electromagnetic field theory, conduction current is equal to
the displacement current that flows between the plates of the capacitor and is present any time that an electric field or voltage varies with time.
what derives from the power that is delivered to the element ?
the energy stored in the capacitor can be derived from the power.
if N inductors are connected in parallel
the equivalent inductance is equal to resistor in parallel. i(t) = sum of all current
if N inductors are connected in series
the equivalent inductance is the sum of the inductance. v(t) = the sum of all voltage
what is open-circuit voltage ?
the external load is disconnected from the source. An electric current will not flow through the circuit.
if only a single storage element is present in the network
the network can be described by a first-order differential equation
voltage divider
the source Vin is divided between the resistor R1 and R2 in direct proportion to their resistances.
What is continuity of voltage ?
the voltage across the capacitor just after a switch moves is the same as the voltage across the capacitor just before that switch moves
if a number of capacitors are connected in series .
their equivalent capacitance is equal to resistor in parallel. v(t) = the sum of all voltage
if a number of capacitors are connected in parallel
their equivalent capacitance is equal to resistor in series. i(t) = the sum of all current
What is purpose of supermesh ?
to avoid introducing the unknown voltage and remove current source between 2 mesh current by mentally. And then add 2 mesh equation.
what is loop analysis?
using KVL to determine a set of loop currents in the circuit. Once these loop currents are known, we can find unknown voltage using Ohm's law.
what is voltage expression form in integration
v(-infinete) = 0
how to find thevenin resistor in the dependent circuit ?
we can give 1mA current source or 1V voltage source in the terminal that we want to find
how to find thevenin resistor in the dependent and independent circuit ?
we must calculate both the open-circuit and short circuit current to calculate the Thevenin equivalent resistance. Also, we must remember that we cannot split the dependent source and its controlling variable.
What is load ?
we wish to find the current, voltage, or power that is delivered to some resistor of the network.
What is general rule for analyzing op-amp circuits ?
we write nodal equations at the op-amp input terminals, using the ideal op-amp model conditions.
what is the general solution of first order equation in RLC circuit ?
x(t) = K_1 + K_2e^(-t/time constant)
Matrix Analysis the inverse of G
|G| is determinant