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3.17 Dependent sources

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Dependent sources.

A dependent source is either a voltage or current source whose value is proportional to someother voltage or current in the circuit. Thus, there are four different kinds of dependent sources; to describe an op-amp, weneed a voltage-dependent voltage source. However, the standard circuit-theoretical model for a transistor contains a current-dependent current source. Dependent sources do not serve as inputs to a circuitlike independent sources. They are used to model active circuits : those containing electronic elements. The RLC circuits we have been considering so far areknown as passive circuits .

Dependent sources

Of the four possible dependent sources, depicted is a voltage-dependent voltage source in the context of a genericcircuit.

[link] shows the circuit symbol for the op-amp and its equivalentcircuit in terms of a voltage-dependent voltage source.

Op-amp

The op-amp has four terminals to which connections can bemade. Inputs attach to nodes a and b , and the output is node c . As the circuit model on the right shows, the op-amp serves as an amplifier for the difference ofthe input node voltages.

Here, the output voltage equals an amplified version of thedifference of node voltages appearing across its inputs. The dependent source model portrays how the op-amp works quitewell. As in most active circuit schematics, the power supply is not shown, but must be present for the circuit model to beaccurate. Most operational amplifiers require both positive and negative supply voltages for proper operation.

Because dependent sources cannot be described as impedances, and because the dependent variable cannot "disappear" when you applyparallel/series combining rules, circuit simplifications such as current and voltage divider should not be applied in mostcases. Analysis of circuits containing dependent sources essentially requires use of formal methods, like the node method . Using the node method for such circuits is notdifficult, with node voltages defined across the source treated as if they were known (as with independent sources). Considerthe circuit shown on the top in [link] .

Feedback op-amp

The top circuit depicts an op-amp in a feedback amplifier configuration. On the bottom is the equivalent circuit, andintegrates the op-amp circuit model into the circuit.

Note that the op-amp is placed in the circuit "upside-down," with its inverting input at the top and serving as the onlyinput. As we explore op-amps in more detail in the next section, this configuration will appear again and again and its usefulness demonstrated. To determine how the output voltage is relatedto the input voltage, we apply the node method. Only two node voltages— v and v out —need be defined; the remaining nodes are across sources or serve as the reference. The node equations are

v v in R v R in v v out R F 0
v out G v R out v out v R F v out R L 0
Note that no special considerations were used in applying the node method to this dependent-source circuit. Solving these tolearn how v out relates to v in yields
R F R out R out G R F 1 R out 1 R in 1 R L 1 R 1 R in 1 R F 1 R F v out 1 R v in
This expression represents the general input-output relation for this circuit, known as the standard feedback configuration . Once we learn more about op-amps , in particular what its typical element values are, the expression will simplifygreatly. Do note that the units check, and that the parameter G of the dependent source is a dimensionless gain.

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
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