The main parameters of the filter
Center Frequency (Center Frequency): The frequency f0 of the passband of the filter, generally f0=(f1+f2)/2, f1 and f2 are the left and right side frequency points of the bandpass or bandstop filter with a relative decrease of 1dB or 3dB. Narrowband filters often use the minimum point of insertion loss as the center frequency to calculate the passband bandwidth.
Cutoff Frequency (Cutoff Frequency): Refers to the right frequency point of the passband of the low-pass filter and the left frequency point of the passband of the high-pass filter. Usually 1dB or 3dB relative loss point to the standard definition. The reference benchmark for relative loss is: the low-pass is based on the insertion loss at DC, and the high-pass is based on the insertion loss at a sufficiently high passband frequency where there is no parasitic stop band.
Passband bandwidth: refers to the width of the spectrum that needs to pass, BW=(f2-f1). f1 and f2 are based on the insertion loss at the center frequency f0.
Insertion Loss: The attenuation caused by the introduction of the filter to the original signal in the circuit is characterized by the loss at the center or cut-off frequency. If the insertion loss is required to be full-band, it must be emphasized.
Ripple (Ripple): refers to the peak value of the insertion loss fluctuating with frequency on the basis of the loss mean curve within the range of 1dB or 3dB bandwidth (cut-off frequency).
Passband Ripple: The variation of insertion loss with frequency in the passband. The in-band fluctuation within the 1dB bandwidth is 1dB.
In-band standing wave ratio (VSWR): An important indicator to measure whether the signal in the passband of the filter is well matched for transmission. Ideal matching VSWR=1:1, VSWR is greater than 1 when there is a mismatch. For an actual filter, the bandwidth that satisfies VSWR less than 1.5:1 is generally smaller than BW3dB, and its proportion to BW3dB is related to the filter order and insertion loss.
Return Loss (Return Loss): The decibel (dB) number of the ratio of the port signal input power to the reflected power, which is also equal to 20Log10ρ, and ρ is the voltage reflection coefficient. The return loss is infinite when the input power is fully absorbed by the port.
Stop band rejection: an important indicator to measure the performance of filter selection. The higher the index, the better the suppression of out-of-band interference signals. There are usually two formulations: one is to ask how much dB is suppressed for a given out-of-band frequency fs, and the calculation method is the attenuation at fs; the other is to propose an index that characterizes the closeness of the amplitude-frequency response of the filter to the ideal rectangle—the rectangular coefficient (KxdB is greater than 1), KxdB=BWxdB/BW3dB, (X can be 40dB, 30dB, 20dB, etc.). The higher the order of the filter, the higher the rectangularity—that is, the closer K is to the ideal value 1, the more difficult it is to make.
Delay (Td): refers to the time required for the signal to pass through the filter, and is numerically the derivative of the diagonal frequency of the transmission phase function, that is, Td=df/dv.
In-band phase linearity: This indicator characterizes the phase distortion introduced by the filter to the transmission signal in the passband. Filters designed with a linear phase response function have good phase linearity.
filter design
For the design of active filters, you can use the tools of chip manufacturers
ADI：
Filter Design Tool | Filter Design Wizard | Analog Devices
TI：
Filter Design Tool (ti.com)
Simulation of Filters
For single-ended filters, the circuit can be simulated using multisim, and the frequency characteristics can be easily viewed using XBP (Bode plot).
For differential circuits, I haven't set up the XBP tool of multisim, and I don't know how to use it. You can use the S(1,2) parameter of ADS to see the frequency situation.
Passive Filter Design
ADS can be used to design passive filters, refer to the following documents.
