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2020 Extra Class study guide: E5A - Resonance and Q: characteristics of
resonant circuits; series and parallel resonance; Q; half-power bandwidth;
phase relationships in reactive circuits

Posted: 31 Jan 2020 06:27 AM PST
http://feedproxy.google.com/~r/kb6nu...m_medium=email


Well, its that time againtime for an update to the No Nonsense Extra Class
License Study Guide! Heres the first section of the first chapter. Comments
welcome!


Resonance is one of the coolest things in electronics. Resonant circuits
are what makes radio, as we know it, possible.

What is resonance? Well, a circuit is said to be resonant when the
inductive reactance and capacitive reactance are equal to one another. That
is to say, when
2Ï€fL = 1/(2Ï€fC)

where L is the inductance in henries and C is the capacitance in farads.

For a given L and a given C, this happens at only one frequency:
f = 1/(2π√(LC))

This frequency is called the resonant frequency.
QUESTION: What is resonance in an LC or RLC circuit? (E5A02)

ANSWER: The frequency at which the capacitive reactance equals the
inductive reactance

Lets calculate a few resonant frequencies, using questions from the Extra
question pool as examples:
QUESTION: What is the resonant frequency of an RLC circuit if R is 22 ohms,
L is 50 microhenries and C is 40 picofarads? (E5A14)

ANSWER: 3.56 MHz
f = 1/(2π√(LC)) = 1/(6.28 × √(50×10-6 × 40×10-12)) = 1/(2.8 × 10-7) = 3.56
MHz

Notice that it really doesnt matter what the value of the resistance is.
The resonant frequency would be the same if R had been 220 ohms or 2.2
Mohms.
QUESTION: What is the resonant frequency of an RLC circuit if R is 33 ohms,
L is 50 microhenries and C is 10 picofarads? (E5A16)

ANSWER: 7.12 MHz
f = 1/(2π√(LC)) = 1/(6.28×√(50×10-6 × 10×10-12)) = 1/(1.4×10-7) = 7.12 MHz

When an inductor and a capacitor are connected in series, the impedance of
the series circuit at the resonant frequency is zero because the reactances
are equal and opposite at that frequency. If there is a resistor in the
circuit, that resistor alone contributes to the impedance. Therefore, the
magnitude of the impedance of a series RLC circuit at resonance is
approximately equal to circuit resistance.
QUESTION: What is the magnitude of the impedance of a series RLC circuit at
resonance? (E5A03)

ANSWER: Approximately equal to circuit resistance

When an inductor and capacitor are connected in parallel, the reactances
are again equal and opposite to one another at the resonant frequency, but
because they are in parallel, the circuit is effectively an open circuit.
Consequently, the magnitude of the impedance of a circuit with a resistor,
an inductor and a capacitor all in parallel, at resonance, is approximately
equal to circuit resistance.
QUESTION: What is the magnitude of the impedance of a parallel RLC circuit
at resonance? (E5A04)

ANSWER: Approximately equal to circuit resistance

Because a parallel LC circuit is effectively an open circuit at resonance,
the magnitude of the current at the input of a parallel RLC circuit at
resonance is very low.
QUESTION: What is the magnitude of the current at the input of a parallel
RLC circuit at resonance? (E5A07)

ANSWER: Minimum

Conversely, he magnitude of the circulating current within the components
of a parallel LC circuit at resonance is high because the circuit within
the loop is effectively a serial resonant circuit.
QUESTION: What is the magnitude of the circulating current within the
components of a parallel LC circuit at resonance? (E5A06)

ANSWER: It is at a maximum

High currents circulating in a resonant circuit can cause the voltage
across reactances in series to be larger than the voltage applied to them.
QUESTION: What can cause the voltage across reactances in a series RLC
circuit to be higher than the voltage applied to the entire circuit?( E5A01)

ANSWER: Resonance

Another consequence of the inductive and capacitive reactances canceling
each other is that there is no phase shift at the resonant frequency.
QUESTION: What is the phase relationship between the current through and
the voltage across a series resonant circuit at resonance? (E5A08)

ANSWER: The voltage and current are in phase



Ideally, a series LC circuit would have zero impedance at the resonant
frequency, while a parallel LC circuit would have an infinite impedance at
the resonant frequency. In the real world, of course, resonant circuits
don’t act this way. Both inductors and capacitors have a series resistance,
even if To describe how closely a circuit behaves like an ideal resonant
circuit, we use the quality factor, or Q. Because the inductive reactance
equals the capacitive reactance at the resonant frequency, the Q of an RLC
parallel circuit is the resistance divided by either inductive or capaciive
reactance, or Q = R/XL or R/XC.
QUESTION: How is the Q of an RLC parallel resonant circuit calculated?
(E5A09)

ANSWER: Resistance divided by the reactance of either the inductance or
capacitance

The Q of an RLC series resonant circuit is the inductive reactance or the
capacitive reactance divided by the resistance, or Q = XL/R or XC/R.
QUESTION: How is the Q of an RLC series resonant circuit calculated? (E5A10)

ANSWER: Reactance of either the inductance or capacitance divided by the
resistance

Basically, the higher the Q, the more a resonant circuit behaves like an
ideal resonant circuit, and the higher the Q, the lower the resistive
losses in a circuit.
QUESTION: Which of the following increases Q for inductors and capacitors?
(E5A15)

ANSWER: Lower losses

But, increasing Q has its drawbacks, too. Increasing Q in a resonant
circuit will increase internal voltages and circulating currents, and the
resonant circuit will have to be made with components that can withstand
these higher voltages and currents.
QUESTION: What is an effect of increasing Q in a series resonant circuit?
(E5A13)

ANSWER: Internal voltages increase

A parameter of a resonant circuit that is related to Q is the half-power
bandwidth. The half-power bandwidth is the bandwidth over which a series
resonant circuit will pass half the power of the input signal and over
which a parallel resonant circuit will reject half the power of an input
signal.

We can use the Q of a circuit to calculate the half-power bandwidth:
BW = f/Q

Let’s look at a couple examples:
QUESTION: What is the half-power bandwidth of a resonant circuit that has a
resonant frequency of 7.1 MHz and a Q of 150? (E5A11)

ANSWER: 47.3 kHz
BW = f/Q = 7.1 × 106/150 = 47.3 × 103 = 47.3 kHz
QUESTION: What is the half-power bandwidth of a resonant circuit that has a
resonant frequency of 3.7 MHz and a Q of 118? (E5A12)

ANSWER: 31.4 kHz
BW = f/Q = 3.5 × 106/118 = 31.4 × 103 = 31.4 kHz

Resonant circuits are often used as impedance-matching circuits. Because BW
= f/Q, increasing the Q of a resonant circuit used for this application has
the effect of decreasing the range of frequencies, or bandwidth, over which
it can match the impedance between two circuits or between a transmitter
and an antenna.
QUESTION: What is the result of increasing the Q of an impedance-matching
circuit? (E5A05)

ANSWER: Matching bandwidth is decreased

The post 2020 Extra Class study guide: E5A Resonance and Q:
characteristics of resonant circuits; series and parallel resonance; Q;
half-power bandwidth; phase relationships in reactive circuits appeared
first on KB6NUs Ham Radio Blog.

In article , rec-radio-amateur-
says...


Well, its that time againtime for an update to the No Nonsense Extra Class
License Study Guide! Heres the first section of the first chapter. Comments
welcome!




The updates should be the start of the year. Having them in the middle
of the year is the worst time. Many exams are given at hamfests. For
the local one this year it is July 11. Just a few days after the change
of the question pool.