( 1 ) Frequency of tank circuit
f = 1 / 2π √ ( LC )
Where L = Inductance of tank circuit
C = Capacitance of tank circuit
( 2 ) Barkhausen criteria
mvAv = 1
Where
mv
= Feedback fraction
Av
= Voltage gain of amplifier without feedback
( 3 ) Voltage gain of positive
feedback amplifier
Avf = Av / (
1 – mvAv )
Where
Avf
= Voltage gain with positive feedback
mv
= Feedback fraction
Av
= Voltage gain without feedback
( 4 ) Frequency of Colpitt
oscillator
f = 1 / 2π √ ( LCT )
Where CT = C1 ‖ C2
= C1 × C2 / ( C1 + C2 )
Feedback
fraction mv = C1 / C2
= Vf / Vout
( 5 ) Frequency of Hartley
oscillator
f = 1 / 2π √ ( CLT )
Where
LT = L1 + L2 + 2M
M = Mutual
Coupling between L1 and L2
Feedback
Fraction mv = L2 / L1
= Vf / Vout
( 6 ) Frequency of Phase
shift oscillator
fo = 1 / 2πRC √ 6
Where
R =
R1 = R2 = R3
C = C1 = C2 = C3
( 7 ) Frequency of Wien
bridge oscillator
f = 1 / 2π √ R1C1R2C2
Where
R1
= R2 = R and C1 = C2 = C
f
= 1 / ( 2π √ R2C2 )
f
= 1 / 2π √ RC
( 8 ) Frequency of Piezo
electric crystal
f = k / t
Where
k = Constant
t =
Thickness of crystal
( 9 ) When the crystal is not vibrating, it is equal
to mounting
capacitance. When the crystal is vibrating, it is equal to R – L – C series circuit.
( 10 ) Q factor of
Crystal
Q =
1 / ( R √ L / C )
( 11 ) Series resonance
frequency of Crystal
fs = 1 / ( 2π √ LC )
( 12 ) Parallel resonance
frequency of Crystal
fp = 1 / ( 2π √ LCT
)
Where
CT = ( C × Cm ) / C + Cm
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