Zr=R, voltage and current have no phase shift

Zl=jwL, current lags voltage T/4

Zc=1/jwC, voltage lags current T/4

Xl=jωl=j2πfL

Xc=1/(jωC)=1/(j2πfC)

X=ωL-1/ωC

series connection

in parallel

ρ=Xl0=Xc0=ω0L=1/ω0C=√L/C

series connection

in parallel

series connection

in parallel

series connection

in parallel

series connection

in parallel

ω0=1/√LC

f0=1/2π√LC=2Δf0.7Q

Physical meaning: Under resonance conditions, the ratio of the energy stored in the loop to the energy consumed

series connection

in parallel

N(f)

The smaller the Q, the wider the passband; the larger the Q, the better the selectivity and the smaller the circuit loss.

The corresponding frequency range when the loop terminal voltage drops to 1/√2 of the maximum value

B = 2Δω0.7 = ω0/Q

B = 2Δf0.7 = f0/Q

The larger Q is, the steeper the change in the phase characteristic curve near ω0 is.

Ideally, the phase-frequency curve is a straight line, which means that the delay for each frequency is fixed to ensure that the signal is not distorted.

series connection

in parallel

Rs: signal source internal resistance; RL: load

QL＜Q

 减小信号源内阻和负载对回路和影响

 负载电阻和信号源内阻小时应采用串联方式

 负载电阻和信号源内阻大时应采用并联方式

 负载电阻信号源内阻不大不小采用部分接入方式

It is advisable to look into any parallel branch between ab to find the resonance

Zab/Zbd = p^2

p = L1/(L1 L2)

p = 1/n = C/C1 = C2/(C1 C2)

I' = pI

Ri' = Ri/p^2

CL' = p^2CL

When the tap is low → high, the equivalent resistance increases by 1/p^2, the parallel resistance increases, and the impact on the Q value is reduced.

RL' = n^2·RL，n = N1/N2=U1/U2

Self-inductance voltage

Mutual inductance voltage

When two currents flow into or out of the corresponding terminals of the two coils at the same time, and the generated magnetic fluxes strengthen each other, the two corresponding terminals are called the same terminals of the two mutual inductance coils.

Both loops are tuned to the signal frequency

All are high Q circuits

A circuit connected to an excitation signal source

The circuit connected to the load

Common impedance consists of two or more circuit components

The ratio of the absolute value of the common reactance (or resistance) of the coupling loop to the geometric mean of the reactance (or resistance) of the same nature in the primary and secondary loops,

The influence of the secondary current on the primary current caused by the electromotive force induced in the primary circuit through the mutual inductance M can be represented by an equivalent impedance Zf1

effect

width between peaks

The larger k is, the farther the distance between the double peaks is, and the greater the concavity is at the resonance point.

It has extremely high operating frequency stability, very steep stopband attenuation characteristics, and very small passband attenuation.

When an alternating electric field is applied to the two pins of a quartz crystal, it will produce mechanical deformation of a certain frequency. This mechanical vibration will generate an alternating electric field.

Usually, the piezoelectric effect is not obvious. However, when the frequency of the alternating electric field reaches a certain value, the amplitudes of the mechanical vibration and the alternating electric field suddenly increase, causing resonance.

No vibration

vibration