Bandpass RLC Network

The following figure shows the parallel form of a bandpass RLC circuit:

Figure 1: Bandpass RLC Network.

The transfer function from input to output voltage is:

The productLCcontrols the bandpass frequency whileRCcontrols how narrow the passing band is. To build a bandpass filter tuned to the frequency 1 rad/s, setL=C=1and useRto tune the filter band.

Analyzing the Frequency Response of the Circuit

波德图方便ol for investigating the bandpass characteristics of the RLC network. Usetfto specify the circuit's transfer function for the values

%|R=L=C=1|:R = 1; L = 1; C = 1; G = tf([1/(R*C) 0],[1 1/(R*C) 1/(L*C)])

G = s ----------- s^2 + s + 1 Continuous-time transfer function.

Next, usebodeto plot the frequency response of the circuit:

bode(G), grid

As expected, the RLC filter has maximum gain at the frequency 1 rad/s. However, the attenuation is only -10dB half a decade away from this frequency. To get a narrower passing band, try increasing values of R as follows:

R1 = 5; G1 = tf([1/(R1*C) 0],[1 1/(R1*C) 1/(L*C)]); R2 = 20; G2 = tf([1/(R2*C) 0],[1 1/(R2*C) 1/(L*C)]); bode(G,'b',G1,'r',G2,'g'），网格传奇（'R = 1','R = 5','R = 20')

The resistor valueR=20gives a filter narrowly tuned around the target frequency of 1 rad/s.

Analyzing the Time Response of the Circuit

We can confirm the attenuation properties of the circuitG2(R=20) by simulating how this filter transforms sine waves with frequency 0.9, 1, and 1.1 rad/s:

t = 0:0.05:250; opt = timeoptions; opt.Title.FontWeight ='Bold'; subplot(311), lsim(G2,sin(t),t,opt), title('W = 1') subplot(312), lsim(G2,sin(0.9*t),t,opt), title('w = 0.9') subplot(313), lsim(G2,sin(1.1*t),t,opt), title('w = 1.1')

The waves at 0.9 and 1.1 rad/s are considerably attenuated. The wave at 1 rad/s comes out unchanged once the transients have died off. The long transient results from the poorly damped poles of the filters, which unfortunately are required for a narrow passing band:

damp(pole(G2))

Pole Damping Frequency Time Constant (rad/TimeUnit) (TimeUnit) -2.50e-02 + 1.00e+00i 2.50e-02 1.00e+00 4.00e+01 -2.50e-02 - 1.00e+00i 2.50e-02 1.00e+00 4.00e+01

Interactive GUI

要分析其他标准电路配置，例如低通和高通RLC网络，请单击下面的链接以启动交互式GUI。在此GUI中，您可以更改R，L，C参数，并实时查看对时间和频率响应的影响。

Open the RLC Circuit GUI

rlc_gui