Useful Formulas and How to solve them for the Extra Exam

These are questions originaly taken from the Advanced Exam pool, most of them are on the current extra exam.


What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 14.25 MHz and a Q of 187?

BW = f / Q, so the bandwidth is 14,250,00 / 187 = 76,203 HZ

What is the Q of a parallel R-L-C circuit if the resonant frequency is 14.225 MHz, L is 3.5 microhenrys and R is 10 kilohms?

Q = R / X for a parallel circuit where X is the circuit reactance and R is the resistance X for inductance is 2 pi f L where f = frequency and L = inductance.
Q = 10,000 / (2 * 3.1416 * 14,225,000* 0.0000035) = 31.96

What is the value of capacitance (C) in a series R-L-C circuit if the circuit resonant frequency is 14.25 MHz and L is 2.84 microhenrys?

C=1/4*pi^2 * f^2 * L 1/4*pi^2*14,250,000^2*.00000284 = .0000000000439239 or 44 picofarads

What is the Q of a parallel R-L-C circuit if the resonant frequency is 3.625 MHz, L is 3 microhenrys and R is 2.2 kilohms?

2200/2*pi*(3,625,000*.000003)=32.1968 or rounding up to a Q of 32

What is the resonant frequency of a parallel R-L-C circuit if R is 4.7 kilohms, L is 2 microhenrys and C is 15 picofarads?

f = 1 / ( 2 pi sqrt(L * C) = 29.06 MHZ

What is the resonant frequency of a series R-L-C circuit if R is 47 ohms, L is 40 microhenrys and C is 200 picofarads?

If Q is at all large, Fr = 1/(6.28 * (the square root of L*C)) 1/(6.28 * (sqrt (.00004 * .000000000,2)))=17.80 Mhz

What is the effective radiated power of a repeater station with 200 watts transmitter power output, 2-dB feed line loss, 2.8-dB duplexer loss, 1.2-dB circulator loss and 7-dBd antenna gain?

For power, 1dB = 1.26, 3dB = 2, 6dB = 4, and 10 dB = 10, the effective gain is 1 dB, so the answer is 252 watts erp.

Here is another way. 1db power ratio is 1.2589:1


How many turns will be required to produce a 5-microhenry inductor using a powdered-iron toroidal core that has an inductance index (A sub L) value of 40?

(1000*sqrt(L/(A sub L))= N

Here is another way

Sqrt (L*(Al*10-9)) = N
Sqrt (5*10-6/40*10-9) = 11.18T
round down to 11 turns.

What is the phase angle between the voltage across and the current through a series R-L-C circuit if Xc is 250 ohms, R is 1 kilohm, and XL is 500ohms?

Ø = tan-1((Xl -Xc)/R)