Electric Circuit Analysis: Unit V: Resonance and coupled circuits
Derive an expression for the resonant frequency of
Resonance circuits
The resonance frequency is calculated 1/2π √1/LC – R2/L2 . A few problems could be added.
DERIVE AN EXPRESSION FOR THE RESONANT FREQUENCY OF:
While
R1 will not affect the resonance frequency, it will influence the
BW. This is a problem frequented in AIR and DD.
Zr
= Total impedance of total combination at resonance.
Z10
= Impedance of original RLC circuit.
ZT
= Z10 . RX / Z10 + RX ; QT
= ZT. XL ; BW = f0 / QT
The
resonance frequency is calculated 1/2π √1/LC – R2/L2 . A
few problems could be added.
(b) Q of the circuit prior to the installation
of ext. load.
=
2π × 4.9103 × 106 × 3.5 × 10-6 / 2.5 = 43.19
(c)
Res. impedance of the circuit prior to the installation of ext. resistance
=
L/CR = 3.5 × 10-6 / 300 × 10-12 × 2.5 = 4666.67 Ω
(d)
Impedance of the res. circuit after the installation of 15 K
=
3559.32 Ω
(e)
Qg of the circuit after installing the ext. resistance
=
3559.32 / 2лƒL = 32.96
(f)
BW prior to the installation of ext. resistance
=
4.9103 × 106 / 43.19 = 113.69 KHz
(g) BW of the circuit after installing the
ext. load
=
4.9103 × 106 / 32.96 = 148.98 KHz
Suppose
if 15 K Ω is reduced to 5 K,
the
new ZT = 4.66667 × 5 / 4.66667 + 5 = 2.41379 K
New
Q = 2.41379 × 103 = 22.35
New
BW = 2.41379 × 106 / 22.35 = 219.67 KHz
In
short, RX↓ Q↓ BW↑ || Very important
Ex.
7 A choke coil has a resistance of 40Ω and a Q of 5 at 1000 Hz. It is connected
in parallel with a variable capacitor to a 10V 1000 Hz a.c supply. Find (a) Xc
for resonance at 1000 KHz. (b) Equivalent impedance as seen by the source at
resonance. (c) Values of L & Cat resonance at 1000 Hz. (d)
Current drawn from the supply at resonance.
At
parallel resonance, the equivalent parallel inductive reactance equal to the
capacitive reactance. j208 is cancelled by -j208.
-j208
at 1000 Hz means 1 / 2πƒ × 208 → 0.76519 μF
j200
at 1000 Hz means 0.03183.
Resonance
impedance = 1040 Ω
Also
by cross check = L / CR = 1040 Ω
Current
drawn at resonance = 10 / 1040 = 9.615 mA
Electric Circuit Analysis: Unit V: Resonance and coupled circuits : Tag: : Resonance circuits - Derive an expression for the resonant frequency of
Electric Circuit Analysis: Unit V: Resonance and coupled circuits
Under Subject
Electric Circuit Analysis
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