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Rev 2.02<br />
Effective Radiated Power<br />
Lets take an example with the following characteristics:<br />
o Power output from radio = 50 watts<br />
o Feed line loss = - 4dB<br />
o Duplexer loss = -2 dB<br />
o Circulator loss = - 1dB<br />
o Antenna Gain =+ 4 dB<br />
First we calculate the overall ERP as follows:<br />
ERP=Transmitter Power Out = +((-4)+(-2)+(-=1)+(+4)) = 50 - 3 dB or 25 watts<br />
Resonant circuits<br />
� In any resonant circuit the X L is equal to the XC at resonance<br />
� In a series resonant circuit the impedance at the resonant frequency is zero<br />
� In a parallel resonant circuit the impedance at resonance is ∞<br />
� In a parallel resonant circuit with perfect components once the circuit is energized it will continue to oscillate<br />
forever with the capacitor charging the inductor then the inductor charging the capacitor. Since our components<br />
are not perfect this will not happen.<br />
Series resonant circuits<br />
Series Resonant Circuits look like a short to the signal source (assuming ideal components) with the only limit on current being<br />
the resistance of the components and any external resistance added in series<br />
Series Resonant Frequency is determined by the following equation with Frequency in Hertz, Inductance in Henries and<br />
Capacity in farads. (or frequency in kHz, inductance in mH and capacity in µ Henries and µH)<br />
1<br />
FR =<br />
2π√(LC)<br />
For a circuit with an inductance of 50 µH and 40 pF<br />
FR = 1/ (2π√(LC)) = 1/(6.28 √(.000050 x .000,000,000,040) = 3,558,812 Hz<br />
or<br />
FR = 1/ (2π√(LC)) = 1/(6.28 √(50 x . 000,040) = 3.559 kHz<br />
Parallel Resonant circuits<br />
Has high output voltage and looks like a high resistance (or in a perfect circuit an open circuit) to the signal source.<br />
Calculating resonant frequency for a parallel inductor and capacitor circuit:<br />
Resonant frequency = 1/ (2π √ (LC) )<br />
Let’s calculate the resonant frequency for a circuit a circuit with a 10 µH inductor and 300 pf capacitor. Remember that this<br />
equation requires the inductance to be in Henries and capacitance in Farads, the resonant frequency answer will be in Hz.<br />
F = 1/ (2π √ (LC) ) = 1/ (2 π √ ((10 ↑-6) * (300 ↑-12)) = 1/ (2 π √(30↑-16))<br />
F= 2,900,000 Hz or 2.9 MHz<br />
If you need to determine which L or C component is needed to resonate at a specific frequency, the following equations can be<br />
used:<br />
L= 1/((2 π F)² C) or C= 1/((2 π F)² L)<br />
Jack Tiley <strong>AD7FO</strong> Page 108 3/15/2009