en>Jonesey95: Fixing deprecated month parameter

2014-09-14T18:04:34Z

71.41.210.146: /* Delta-v */ Added limiting cost.

2014-01-22T07:04:08Z

Delta-v: Added limiting cost.

← Older revision		Revision as of 09:04, 22 January 2014
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	The ~~author~~ is called ~~Wilber Pegues~~. ~~Her family members lives~~ in ~~Ohio~~. ~~Office supervising~~ is ~~my occupation~~. The ~~favorite hobby for him~~ and ~~his kids~~ is to ~~play lacross~~ and ~~he would~~ by ~~no means give it up~~.<br><br>~~Feel free~~ to ~~visit my homepage~~; ~~tarot card readings~~, [~~http~~://~~kjhkkb~~.~~net~~/xe/~~notice~~/~~374835 sites~~],		[[Image:Current division example.svg\|thumbnail\|250px\|Figure 1: Schematic of an electrical circuit illustrating current division. Notation ''R<sub>T<sub>.</sub></sub>'' refers to the ''total'' resistance of the circuit to the right of resistor ''R<sub>X</sub>''.]]

			In [[electronics]], a '''current divider ''' is a simple [[linear circuit]] that produces an output [[Electric current\|current]] (''I''<sub>X</sub>) that is a fraction of its input current (''I''<sub>T</sub>). '''Current division''' refers to the splitting of current between the branches of the divider. The currents in the various branches of such a circuit will always divide in such a way as to minimize the total energy expended.

			The formula describing a current divider is similar in form to that for the [[voltage divider]]. However, the ratio describing current division places the impedance of the unconsidered branches in the [[numerator]], unlike voltage division where the considered impedance is in the numerator. This is because in current dividers, total energy expended is minimized, resulting in currents that go through paths of least impedance, therefore the inverse relationship with impedance. On the other hand, voltage divider is used to satisfy [[Kirchhoff's circuit laws#Kirchhoff's voltage law (KVL)\|Kirchhoff's Voltage Law]]. The voltage around a loop must sum up to zero, so the voltage drops must be divided evenly in a direct relationship with the impedance.

			To be specific, if two or more [[Electrical impedance\|impedance]]s are in parallel, the current that enters the combination will be split between them in inverse proportion to their impedances (according to [[Ohm's law]]). It also follows that if the impedances have the same value the current is split equally.

			==Current divider==
			A general formula for the current ''I<sub>X</sub>'' in a resistor ''R<sub>X</sub>'' that is in parallel with a combination of other resistors of total resistance ''R<sub>T</sub>'' is (see Figure 1):

			:<math>I_X = \frac{R_T}{(R_X+R_T)}I_T \ </math>
			where ''I<sub>T</sub>'' is the total current entering the combined network of ''R<sub>X</sub>'' in parallel with ''R<sub>T</sub>''. Notice that when ''R<sub>T</sub>'' is composed of a [[Series_and_parallel_circuits#Parallel_circuits\|parallel combination]] of resistors, say ''R<sub>1</sub>'', ''R<sub>2</sub>'', ... ''etc.'', then the reciprocal of each resistor must be added to find the total resistance ''R<sub>T</sub>'':
			:<math> \frac {1}{R_T} = \frac {1} {R_1} + \frac {1} {R_2} + \frac {1}{R_3} + ... \ . </math>

			==General case==
			Although the resistive divider is most common, the current divider may be made of frequency dependent [[Electrical impedance\|impedance]]s. In the general case the current I<sub>X</sub> is given by:
			:<math>I_X = \frac{Z_T} {Z_X+Z_T}I_T \ ,</math><ref>{{cite book \|first1=Charles \|last1=Alexander\| first2=Matthew \|last2=Sadiku\| title=Fundamentals of Electric Circuits\|year=2007\|publisher=McGraw-Hill\|location=New York, NY\|isbn=978-0-07-128441-7\|page=392}}</ref>

			==Using Admittance==
			Instead of using [[Electrical impedance\|impedance]]s, the current divider rule can be applied just like the [[voltage divider]] rule if [[admittance]] (the inverse of impedance) is used.
			:<math>I_X = \frac{Y_X} {Y_{Total}}I_T</math>
			Take care to note that Y<sub>Total</sub> is a straightforward addition, not the sum of the inverses inverted (as you would do for a standard parallel resistive network). For Figure 1, the current I<sub>X</sub> would be
			:<math>I_X = \frac{Y_X} {Y_{Total}}I_T = \frac{\frac{1}{R_X}} {\frac{1}{R_X} + \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}}I_T</math>

			===Example: RC combination===
			[[Image:Low pass RC filter.PNG\|thumbnail\|220px\|Figure 2: A low pass RC current divider]]
			Figure 2 shows a simple current divider made up of a [[capacitor]] and a resistor. Using the formula above, the current in the resistor is given by:

			::<math> I_R = \frac {\frac{1}{j \omega C}} {R + \frac{1}{j \omega C} }I_T </math>
			:::<math> = \frac {1} {1+j \omega CR} I_T \ , </math>
			where ''Z<sub>C</sub> = 1/(jωC) '' is the impedance of the capacitor and <var>j</var> is the [[imaginary unit]].

			The product ''τ = CR'' is known as the [[time constant]] of the circuit, and the frequency for which ωCR = 1 is called the [[corner frequency]] of the circuit. Because the capacitor has zero impedance at high frequencies and infinite impedance at low frequencies, the current in the resistor remains at its DC value ''I<sub>T</sub>'' for frequencies up to the corner frequency, whereupon it drops toward zero for higher frequencies as the capacitor effectively [[short-circuit]]s the resistor. In other words, the current divider is a [[low pass filter]] for current in the resistor.

			==Loading effect==
			[[File:Current Division.svg\|thumbnail\|300px\|Figure 3: A current amplifier (gray box) driven by a Norton source (''i<sub>S</sub>'', ''R<sub>S</sub>'') and with a resistor load ''R<sub>L</sub>''. Current divider in blue box at input (''R<sub>S</sub>'',''R<sub>in</sub>'') reduces the current gain, as does the current divider in green box at the output (''R<sub>out</sub>'',''R<sub>L</sub>'')]]
			The gain of an amplifier generally depends on its source and load terminations. Current amplifiers and transconductance amplifiers are characterized by a short-circuit output condition, and current amplifiers and transresistance amplifiers are characterized using ideal infinite impedance current sources. When an amplifier is terminated by a finite, non-zero termination, and/or driven by a non-ideal source, the effective gain is reduced due to the '''loading effect''' at the output and/or the input, which can be understood in terms of current division.

			Figure 3 shows a current amplifier example. The amplifier (gray box) has input resistance ''R<sub>in</sub>'' and output resistance ''R<sub>out</sub>'' and an ideal current gain ''A<sub>i</sub>''. With an ideal current driver (infinite Norton resistance) all the source current ''i<sub>S</sub>'' becomes input current to the amplifier. However, for a [[Norton's theorem\|Norton driver]] a current divider is formed at the input that reduces the input current to

			::<math>i_{i} = \frac {R_S} {R_S+R_{in}} i_S \ , </math>

			which clearly is less than ''i<sub>S</sub>''. Likewise, for a short circuit at the output, the amplifier delivers an output current ''i<sub>o</sub>'' = ''A<sub>i</sub> i<sub>i</sub>'' to the short-circuit. However, when the load is a non-zero resistor ''R<sub>L</sub>'', the current delivered to the load is reduced by current division to the value:

			::<math>i_L = \frac {R_{out}} {R_{out}+R_{L}} A_i i_{i} \ . </math>

			Combining these results, the ideal current gain ''A<sub>i</sub>'' realized with an ideal driver and a short-circuit load is reduced to the '''loaded gain''' ''A<sub>loaded</sub>'':

			::<math>A_{loaded} =\frac {i_L} {i_S} = \frac {R_S} {R_S+R_{in}}</math> <math> \frac {R_{out}} {R_{out}+R_{L}} A_i \ . </math>

			The resistor ratios in the above expression are called the '''loading factors'''. For more discussion of loading in other amplifier types, see [[Voltage division#Loading effect\|loading effect]].

			===Unilateral versus bilateral amplifiers===
			[[Image:H-parameter current amplifier.PNG\|thumbnail\|300px\|Figure 4: Current amplifier as a bilateral two-port network; feedback through dependent voltage source of gain β V/V]]
			Figure 3 and the associated discussion refers to a [[Electronic amplifier#Unilateral or bilateral\|unilateral]] amplifier. In a more general case where the amplifier is represented by a [[two-port network\|two port]], the input resistance of the amplifier depends on its load, and the output resistance on the source impedance. The loading factors in these cases must employ the true amplifier impedances including these bilateral effects. For example, taking the unilateral current amplifier of Figure 3, the corresponding bilateral two-port network is shown in Figure 4 based upon [[Two-port network#Hybrid parameters (h-parameters)\| h-parameters]].<ref>The [[Two-port network#Hybrid parameters (h-parameters)\|h-parameter two port]] is the only two-port among the four standard choices that has a current-controlled current source on the output side.</ref> Carrying out the analysis for this circuit, the current gain with feedback ''A<sub>fb</sub>'' is found to be

			::<math> A_{fb} = \frac {i_L}{i_S} = \frac {A_{loaded}} {1+ {\beta}(R_L/R_S) A_{loaded}} \ . </math>

			That is, the ideal current gain ''A<sub>i</sub>'' is reduced not only by the loading factors, but due to the bilateral nature of the two-port by an additional factor<ref>Often called the ''improvement factor'' or the ''desensitivity factor''.</ref> ( 1 + β (R<sub>L</sub> / R<sub>S</sub> ) A<sub>loaded</sub> ), which is typical of [[negative feedback amplifier]] circuits. The factor β (R<sub>L</sub> / R<sub>S</sub> ) is the current feedback provided by the voltage feedback source of voltage gain β V/V. For instance, for an ideal current source with ''R<sub>S</sub>'' = ∞ Ω, the voltage feedback has no influence, and for ''R<sub>L</sub>'' = 0 Ω, there is zero load voltage, again disabling the feedback.

			==References and notes==
			<references/>
			== See also ==

			* [[Voltage divider]]
			* [[Resistor]]
			* [[Ohm's law]]
			* [[Thévenin's theorem]]
			* [[Voltage regulation]]

			== External links ==
			*[http://utwired.engr.utexas.edu/rgd1/lesson05.cfm University of Texas: Notes on electronic circuit theory]

			[[Category:Analog circuits]]
			[[Category:Electronics]]
			[[Category:Electric current]]

en>Teapeat at 17:04, 24 June 2012

2012-06-24T17:04:10Z

New page

The author is called Wilber Pegues. Her family members lives in Ohio. Office supervising is my occupation. The favorite hobby for him and his kids is to play lacross and he would by no means give it up.<br><br>Feel free to visit my homepage; tarot card readings, [http://kjhkkb.net/xe/notice/374835 sites],

Bi-elliptic transfer - Revision history

en>Jonesey95: Fixing deprecated month parameter

71.41.210.146: /* Delta-v */ Added limiting cost.

en>Teapeat at 17:04, 24 June 2012