A voltage divider in terms of a conductance

In summary, a voltage divider is a circuit that divides an input voltage into smaller output voltages using resistors connected in series. Conductance is the measure of a material's ability to conduct electrical current and is the inverse of resistance. In a voltage divider, the conductance of each resistor determines the amount of current that will flow through it, affecting the output voltage. Common applications of a voltage divider include providing specific output voltages, measuring unknown voltages, and controlling amplifier gain. The accuracy of a voltage divider depends on the precision and stability of the resistors used, as well as temperature and supply voltage. Changes in these factors can affect the conductance of the resistors and the output voltage of the divider.
  • #1
bitrex
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I am looking at the following application note that goes into nodal analysis of op amps: http://www.maxim-ic.com/appnotes.cfm/an_pk/1939/ and down at the bottom where they're analyzing the Wien bridge oscillator the equation at the negative input of the op-amp taken from the output in terms of conductance is Gf/(Gi+Gf). I'm not sure how they got that - if expressed in terms of resistances that voltage divider is Ri/(Rf+Ri). How does one change the equation for a voltage divider in terms of resistance to terms of conductance?
 
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  • #2
bitrex said:
I am looking at the following application note that goes into nodal analysis of op amps: http://www.maxim-ic.com/appnotes.cfm/an_pk/1939/ and down at the bottom where they're analyzing the Wien bridge oscillator the equation at the negative input of the op-amp taken from the output in terms of conductance is Gf/(Gi+Gf). I'm not sure how they got that - if expressed in terms of resistances that voltage divider is Ri/(Rf+Ri). How does one change the equation for a voltage divider in terms of resistance to terms of conductance?

In this expression, Ri/(Rf+Ri), substitute:

1/Gf for Rf
1/Gi for Ri

then simplify and you should get the voltage divider formula in terms of conductance.
 
  • #3


The equation for a voltage divider in terms of conductance can be derived from Ohm's Law, where conductance (G) is the reciprocal of resistance (R). Therefore, the equation for a voltage divider in terms of conductance can be written as G1/(G1+G2) where G1 and G2 are the conductances of the two resistors in the circuit. This can also be written as 1/(1+G2/G1).

In the application note that you mentioned, the conductances (Gf and Gi) are being used instead of resistances (Rf and Ri) in the voltage divider equation. This is because the circuit is being analyzed using nodal analysis, which is a method that uses conductances instead of resistances.

To change the voltage divider equation from terms of resistance to terms of conductance, simply replace the resistances with their corresponding conductances in the equation. This can be done using the relationship G=1/R. So, the equation for a voltage divider in terms of conductance would be Gf/(Gi+Gf) as shown in the application note.
 

Related to A voltage divider in terms of a conductance

1. What is a voltage divider?

A voltage divider is a simple circuit that divides an input voltage into smaller output voltages. It consists of two or more resistors connected in series, where the output voltage is taken from the junction between the resistors.

2. What is conductance?

Conductance is the measure of a material's ability to conduct electrical current. It is the inverse of resistance, and is measured in siemens (S) or mhos (℧).

3. How does a voltage divider work in terms of conductance?

In a voltage divider, the conductance of each resistor determines the amount of current that will flow through it. The higher the conductance, the more current will flow through that resistor, resulting in a higher output voltage at the junction between the resistors.

4. What are the applications of a voltage divider in terms of conductance?

A voltage divider is commonly used in electronic circuits to provide a specific output voltage, such as in sensor circuits, power supplies, and audio amplifiers. It can also be used to measure unknown voltages or to control the gain of an amplifier.

5. What factors affect the accuracy of a voltage divider in terms of conductance?

The accuracy of a voltage divider depends on the precision and stability of the resistors used, as well as the temperature and supply voltage. Any changes in these factors can affect the conductance of the resistors and therefore the output voltage of the divider.

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