Fraction Simplification of Impedances and Resistances

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In summary, the person is trying to simplify a transfer function with the equation H(jw)=ZL/R+ZL where ZL is the impedance of an inductor and R is the impedance of a resistor. They suggest simplifying it to ZL(1/R+1) but note that there may be some issues with the units. Another equation is given with the variables a, b, and f, where f represents frequency and 2pi*f represents the reactance of the inductor. The person is seeking help in simplifying this equation.
  • #1
Jordash
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My algebra is really rusty, anyway I'm trying to simplify a Transfer Function so I have

H(jw)=ZL/R+ZL so ZL is the impedance of an inductor and R is the impedance of the Resistor, my question is how would I go about simplifying that transfer function into it's simplest form?

Thanks,

Jordan
 
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  • #2
Well you could do ZL/R+ZL = ZL(1/R + 1) if that is a help.
But there is something odd about ZL/R+ZL. The first term has no units while the second has units of ohms.

I don't know what a "transfer function" is so I'm not much help!
 
  • #3
Let me throw another one out there to hopefully make it easier to understand (don't worry about the transfer function)

so 2.2e3/2.2e3+i2pi10e-3

How would that be simplified or in simpler terms

a/a+b

How would you simplify that

The problem above would be i*2pi*f*L/R+i*2pi*f*L

f is the frequency and 2pi*f would give us the reactance of the Inductor so I'm trying to figure out how to simplify everything.
 

FAQ: Fraction Simplification of Impedances and Resistances

What is the purpose of simplifying fractions in impedances and resistances?

Simplifying fractions in impedances and resistances allows for easier mathematical calculations and helps to better understand the relationships between components in an electrical circuit.

How do you simplify a fraction in impedance?

To simplify a fraction in impedance, both the numerator and denominator must be divided by their greatest common factor (GCF). This will result in a simplified fraction with the smallest possible values for both the numerator and denominator.

Why is it important to simplify fractions in resistances?

Simplifying fractions in resistances allows for easier comparison between different components in a circuit. It also helps to identify the dominant resistances and their effects on the overall circuit.

What is the difference between simplifying fractions in impedances and resistances?

Simplifying fractions in impedances involves complex numbers and takes into account both the real and imaginary parts of the impedance. On the other hand, simplifying fractions in resistances only involves real numbers and is focused on reducing the overall resistance in a circuit.

What are some common mistakes to avoid when simplifying fractions in impedances and resistances?

Some common mistakes to avoid include forgetting to divide both the numerator and denominator by the GCF, incorrectly identifying the dominant resistances or impedances, and failing to simplify the fractions to their smallest possible values.

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