AC2 Fundamentals Unit 3 – Parallel Resonance
Exercise 2 – Q and Bandwidth
EXERCISE OBJECTIVE
When you have completed this exercise, you will be able to calculate the Q and the bandwidth of
a parallel resonant circuit by using standard formulas. You will verify your results with an
oscilloscope.
DISCUSSION
- Resonant circuit selectivity is characterized by a factor called Q.
- The Q of an individual inductor is the inductive reactance divided by the internal resistance
of the inductor. - This internal resistance can be represented as an equivalent parallel resistance (RLP) found by
using the equation RLP = Q^2 x RL. - Practical parallel resonant circuits have a current limiting resistor in series with the signal
generator, prior to the LC parallel network. Here the overall circuit Q is a much lower value
than the Q of the inductor. - Reducing the above circuit to a simple parallel resonant circuit produces an equivalent shunt
resistance (RE). The Q is then calculated by dividing RE by XL (RE/XL). RE is the parallel
combination of (RGEN + R 1 ) and RLP. - The bandwidth (B) of a resonant circuit defines its selectivity.
- Bandwidth is determined by the upper and lower cutoff frequencies of the circuit.
B = f 2 − f 1 - Upper and lower cutoff frequencies occur where circuit voltage is 3 dB down from the
maximum voltage (VRESON). - The higher the Q the smaller the bandwidth. B = fr/Q
- Q can be calculated from the circuit bandwidth. Q = fr/B