The working principle of frequency selective amplifier and the frequency characteristics of double T bridge-EEWORLD

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The working principle of frequency selective amplifier and the frequency characteristics of double T bridge

The frequency selective amplifier selects a desired frequency signal from a variety of frequency input signals and amplifies it. The block diagram shown in the figure below can constitute a frequency selective amplifier circuit, where block K is the basic amplifier circuit and block F is the frequency selective negative feedback network. Therefore, the frequency selective amplifier is essentially a negative feedback circuit with frequency selective function. The closed loop gain of the circuit is
KF=K/(1+FK)
where: K=UO/Ui is the open loop gain and
F=UF/UO is the feedback coefficient

Generally, RC frequency selection network is used to realize the selection period. Figure (b) shows the curve (frequency characteristics) of the feedback coefficient F changing with the frequency f. When f=fo, F=0. Therefore, for the resonant frequency fo, there is no negative feedback in the amplifier circuit, so KF=K, and the output voltage of the amplifier is the largest at this time. As the frequency moves away from fo, F increases rapidly, and the corresponding KF also decays to zero quickly, as shown in Figure C above. Therefore, the output voltage of other useless frequencies that deviate from the fo point is also very small. As for the decay speed of KF, it mainly depends on the frequency selection characteristics of the feedback network. Usually, the RC frequency selection network of the double T bridge is used. In actual use, there are two most commonly used types:

One is an asymmetric double T bridge as shown in the figure above. Assuming that the power supply internal resistance RS=0 and the load RL=00, the calculation formula is as follows:
Resonant angular frequency ωO=1/RC ------------------------- 1.
Quality factor Q=[1/2(1+a)]=[fo/2△fo.7] --------- 2.
The mode and amplitude angles of the transmission coefficient (feedback coefficient) are:

--------------------- 3 Formula
φ =arctg1/QY
Where: Y=σ-(1/σ) is the generalized detuning coefficient
σ=f/fo is the relative detuning coefficient ----------------------- 4 Formula
2△fo.7 is the bandwidth of the half-power point
. It can be seen from Formula 2 that for a fixed resonant frequency fo, the larger the Q, the narrower the passband; conversely, the smaller the Q, the wider the passband. Therefore, the size of Q can reflect the selectivity of the twin-T network. The advantage of this twin-T bridge is that the Q is large, but the input impedance is low, the output impedance is high, and it is inconvenient to connect to the amplifier. Due to the different parameters of the bridge arm, the selection and adjustment also bring troubles. Only when the selectivity requirements are high, the asymmetric twin-T circuit is used. Please refer to the top figure for the input, output impedance and phase angle changes of this circuit. Among them, a is usually selected (0.1-0.2) to obtain a larger Q value.
The second type is a symmetrical twin-T circuit, as shown in Figure-3 below, and the calculation formula is as follows:

Resonant frequency: ω0=

Quality factor: Q=

Obviously, Q is related to n. When n=1, Qmax=0.25, but it is inconvenient to adjust. For the convenience of adjustment, n=0.5 is often selected, corresponding to the three resistors with equal values; or n=2 is selected, corresponding to the three capacitors with equal values. Since the symmetrical twin-T bridge is convenient in selecting components and adjusting, it is widely used.
The correction method of the asymmetry of the transmission characteristics:
In actual use, since RS≠O and RL≠OO and sometimes the twin-T network and the amplifier use AC coupling, for example, in the case of Figure 4 (A), the signal source (ES and RS) is coupled with the twin-T through CS. Since the capacitive reactance 1/ωCS is infinite when the frequency is zero, F=O; when the frequency is very high, the capacitive reactance of CS, C2, and C3 is very small, and F is approximately RL/(RL+RS); since ZS and RL do not affect the resonant frequency, F=0 when f=fo; therefore, the curve of F changing with frequency is shown in Figure 4 (B). It can be seen from the figure that the transmission characteristics are asymmetric.

The existence of Z3 and RL not only distorts the amplitude-frequency characteristic of F, but also makes its phase-frequency characteristic asymmetric. If the phase shift near the resonance point exceeds
π/2, coupled with the effect of some additional phase shift, positive feedback will be introduced in this closed-loop amplifier circuit, causing self-oscillation. In order to eliminate this undesirable phenomenon, capacitor CL is connected in parallel at both ends of RL in circuit diagram 4 (A). Under the action of CL, the amplitude and phase characteristics of F can be corrected as shown in Figure 4 (B). When correcting the phase, the following relationship should be satisfied:
R1C1=R2C2=RLCL=RSCS
R1R2=（1+n）RLRS
If the coupling capacitor is connected to the load end, capacitor CS must be connected in parallel at the input ends 1 and 1'. The ideal correction condition is still the same as the above relationship
. If the double T and the amplifier are directly coupled, CS or CL does not need to be connected. At this time, the symmetric conditions of the amplitude and phase shift characteristics of F can be simplified to:
R1R2=（1+n)RSRL
R1C1=R2C2
It must be noted that: (1) The double T network is directly coupled with the amplifier. Although the selectivity is higher, the DC operating point will be affected and it is difficult to adjust.
(2) The internal resistance ZS should be minimized and the load ZL should be increased as much as possible, otherwise the selectivity of the twin-T will be significantly reduced. Therefore, the basic amplifier circuit should be connected to an emitter follower or source follower before and after to meet the requirements of the twin-T network. (3) Under the influence of the error of the Yuanbo parameter, the balance condition of the twin-T will be destroyed, causing the amplitude-frequency and phase-frequency characteristics to change. Therefore, the components of the twin-T network should be strictly selected according to specific requirements, with good temperature characteristics and stable operation, and they must be aged.

Figure 4 (A)

Figure 4 (B)

Figure 4 (C)

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