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Rev 2.02<br />
Example 2:<br />
To find the angle, θ for a triangle with a side X value of 3 and a side Y value of 4:<br />
Tangent of θ = 4 / 3 or 1.333 To find the angle enter 1.333 into your calculator and press the Arc Tan(or Tan^-1 on<br />
some calculators) key which will show you 53.03°<br />
Example 3:<br />
To find the angle, θ for a triangle with a side X value of 12 and a side Y value of 12<br />
Tangent of θ = 12/12 or 1 To find the angle enter 1 into your calculator and press the Arc Tan key which will<br />
show you 45.0°<br />
Reactance (AC resistance of capacitors and inductors)<br />
Capacitors and inductors exhibit a resistance to current flow much like a resistor but with values that change with<br />
the frequency of the applied circuit.<br />
The AC resistance of a capacitor is called capacitive reactance (Xc) and is calculated using the formula:<br />
Xc= 1/(2π x F x C) with C in µF and F in MHz<br />
Examples:<br />
Find the capacitive reactance of a 1 µf capacitor at 200 Hz<br />
Xc= 1/(2π x F x C) or Xc= 1/(6.28 x .0002 x 1) or Xc= 796 Ω<br />
Find the Capacitive reactance of a 10 PF capacitor at 7 MHz<br />
Xc= 1/(2π x F x C) or Xc= 1/(6.28 x 7.0 x 10 ^-6 ) or Xc= 2,275 Ω<br />
The AC resistance of an Inductor is called Inductive reactance (XL) and is calculated using the formula:<br />
XL= 2π x F x L with L in µH and F in MHz<br />
Examples:<br />
Find the inductive reactance of a 1 µH inductor at 100 MHz<br />
XL= 2π x F x L or XL= 6.28 x 100 x 1 or XL= 628 Ω<br />
Find the inductive reactance of a 100 µH inductor at 7 MHz<br />
XL= 2π x F x L or XL= 6.28 x 7 x 100 or XL= 4,396 Ω<br />
Circuit Impedance<br />
The term Impedance refers to the equivalent circuit resistance in ohms for a circuit consisting of resistance and<br />
capacitive reactance and / or inductive reactance. To solve these problems for series circuits we use a rectangular<br />
coordinate graph and basic algebra and trigonometry. When working with complex circuits containing resistance<br />
and reactance, the reactive components are shown with a lower case j prefix. Inductive reactance is shown with a<br />
+j prefix and capacitive reactance with a –j prefix.<br />
Rectangular Coordinate System<br />
When solving problems involving impedance and phase angle of AC series circuits we show the circuit element<br />
values in a rectangular format. The rectangular format consists of a horizontal line intersected at 90° by a vertical<br />
line. Values on the horizontal or X axis are positive to the right of the vertical line and negative to the left. Values<br />
on the vertical or Y axis are positive above the X axis and Negative below the X axis.<br />
Jack Tiley <strong>AD7FO</strong> Page 41 3/15/2009