MindMap Gallery High Frequency Electronic Circuit Chapter 2 Frequency Selective Network
A mind map of the frequency selection network part of high-frequency electronic circuits, including sinusoidal steady-state analysis, LC resonant circuit, equivalent exchange of series and parallel impedances, and impedance changes when the circuit taps, etc.
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This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
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Chapter 2 Frequency Selective Network
Sinusoidal Steady State Analysis
RLC vector
R
Zr=R, voltage and current have no phase shift
L
Zl=jwL, current lags voltage T/4
C
Zc=1/jwC, voltage lags current T/4
impedance
Resistance
Xl=jωl=j2πfL
Resistance
Xc=1/(jωC)=1/(j2πfC)
LC resonant circuit
Loop impedance
Series Zs=R jX
X=ωL-1/ωC
Parallel connection Zp=L/C(R jX)
Resonance conditions
The total reactance of the loop X=0
series connection
X=ωL-1/ωC=0
in parallel
B=ωC-1/ωL=0
Characteristic impedance
ρ=Xl0=Xc0=ω0L=1/ω0C=√L/C
Rectangle factor
K0.1=2Δf0.1/2Δf0.7
Generalized detuning
Loop detuning size ξ
series connection
in parallel
Resonance characteristics
Resonant impedance
series connection
Z=R jX=R (pure resistance, and take the big and small values)
Resonance resistance: R=R
in parallel
Y=CR/L=Gp=1/Rp (pure conductivity, and take the minimum value)
Resonance resistance: Rp=L/CR=Qp·ωpL=Qp·1/ωpC
Resonant current
series connection
I = Vs/R (reach maximum)
in parallel
|Icp|=|ILp|=Qp|I|
current resonance
Resonant voltage
series connection
|Vc|=|Vl|=Q|Vs|
voltage resonance
in parallel
V0=L/(CR)·Is (reach maximum)
Resonant frequency
ω0=1/√LC
series connection
ω<ω0: The line impedance is capacitive
ω>ω0: The line impedance is inductive
in parallel
ω<ωp: Line impedance is inductive
ω>ωp: The line impedance is capacitive
f0=1/2π√LC=2Δf0.7Q
Quality factor
Physical meaning: Under resonance conditions, the ratio of the energy stored in the loop to the energy consumed
series connection
Q=ω0L/R=1/ω0CR=ρ/R=1/R·√L/C
in parallel
Qp=ωpL/R=1/ωpCR=ρ/R=1/R·√L/C
Loop inherent quality factor Qp=Rp/ωpL=Rp·ωpC
resonance curve
N(f)
Series:Current Ratio
Parallel: voltage ratio
The smaller the Q, the wider the passband; the larger the Q, the better the selectivity and the smaller the circuit loss.
Passband
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
Phase frequency characteristic curve
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.
Loaded Q value
series connection
QL=ω0L/(R Rs RL): Series resonant tank is suitable for low internal resistance power supply (ideal voltage source)
in parallel
: Parallel resonant circuit is suitable for high internal resistance power supply (ideal current source)
Rs: signal source internal resistance; RL: load
QL<Q
Equivalent interchange of series and parallel impedances Impedance change when tapping the loop
Equivalent interchange of series and parallel impedances
Parallel impedance --> Series impedance
Series impedance --> parallel impedance
Other forms of parallel resonant circuits
Zp = (ωpL)^2/(R1 R2) = 1/(R1 R2)(ωpC)^2
The impedance at resonance can be determined by the resistance of the two parallel branches and the reactance of either branch.
Impedance transformation of tapped parallel circuit
Purpose of tapping
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
Access coefficient p=partial access voltage/circuit voltage
Inductor tapped parallel resonant circuit
It is advisable to look into any parallel branch between ab to find the resonance
When resonating, when viewed from any two points of the loop, the loop is purely resistive.
Tap low → high: Z increases by 1/p^2
Tap high → low: Z decreases by p^2
Zab/Zbd = p^2
p = L1/(L1 L2)
Capacitor-tapped parallel resonant circuit
p = 1/n = C/C1 = C2/(C1 C2)
Reduction of current source
I' = pI
Ri' = Ri/p^2
Reduction of load capacitance
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.
transformer
Transformer impedance transformation
RL' = n^2·RL,n = N1/N2=U1/U2
Coupling coefficient
The relationship between voltage and current on coupled inductor
Self-inductance voltage
Mutual inductance voltage
The same terminal of the mutual induction coil
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.
coupling loop
Overview
A coupling loop is a network formed by two or more circuits. There must be a common impedance between the two circuits to complete the coupling effect.
double tuned loop
Both loops are tuned to the signal frequency
All are high Q circuits
primary circuit
A circuit connected to an excitation signal source
secondary circuit
The circuit connected to the load
complex coupling
Common impedance consists of two or more circuit components
Coupling coefficient k
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,
Reflected impedance/coupling impedance
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
When the mutual inductance M is small, the reflected impedance is also very small, and the secondary loop has minimal influence on the primary loop current, which is close to non-existence of the secondary loop.
When M=0, the reflected impedance is 0, which becomes a single loop situation.
When Z22 is very large, even if M is quite large, the reflected impedance is still very small, and the impact on the primary loop is also very small.
Frequency characteristics of coupled oscillation circuit
width between peaks
Δf1/f0 = k
The larger k is, the farther the distance between the double peaks is, and the greater the concavity is at the resonance point.
Other forms of filters
quartz crystal filter
Q is extremely large
It has extremely high operating frequency stability, very steep stopband attenuation characteristics, and very small passband attenuation.
Piezoelectric effect
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.
piezoelectric oscillation
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.
Equivalent circuit and oscillation frequency
No vibration
Plate capacitor C0
vibration
The inertia of vibration is the inductance L0
The elasticity of the chip is equivalent to the capacitance C0
The friction loss of the wafer is equivalent to the resistance rq
Generally works in series resonance state
ceramic filter
surface acoustic wave filtering
Frequency selection: select the required frequency components and filter out the unnecessary frequency components