## Insertion loss

Equal to the difference in dB power measured at the filter input and at the filter output. The power measured at the filter input is equal to the measured power when the filter is replaced by a properly matched power meter or network analyzer. The input impedance of the measuring instrument should be equal to the characteristic impedance of the filter or system. Unless otherwise specified, Mini-Circuits’ filters are designed for 50Ω systems. Similarly, the power measured at the filter output is equal to the measured power when the filter is terminated by the same measuring instrument as discussed. The insertion loss will be equal to the sum of three loss factors. One is the loss due to the impedance mismatch at the filter input, the second is due to the mismatch at the filter output, and the third is due to the dissipative loss associated with each reactive element within the filter.

## Pass-band

Equal to the frequency range for which the filter insertion loss is less than a specified value. For example, most of the Mini-Circuits’ low-pass filter models are specified to have a maximum insertion loss value of 1 dB within the pass-band.

## Stop-band

Equal to the frequency range for which the filter insertion loss is greater than a specified value. For example, most of the Mini-Circuits’ low-pass filter models are characterized by the frequency range where the insertion loss is greater than 20 dB and 40 dB in the stop-band. These two values are arbitrary; they could easily have been chosen for some other values. The purpose for selecting 20 dB and 40 dB is two-fold. One is to provide the design engineer with a simple means to calculate the frequency selectivity of the filter. The second is to allow a quick calculation of the suitability of the filter in a particular situation. Since 20 dB or 40 dB represent sufficient loss requirements in many systems, these values were chosen. The data in this handbook provides actual loss values as a function of frequency. For many Mini-Circuit filters the stop-band losses can exceed 60 dB.

## Cut-off frequency, f_{co}

The frequency at which the filter insertion loss is equal to 3 dB. It is a very convenient point for expressing the pass-band and stop-band boundary points. In addition, it allows a convenient means to normalize the frequency response of a filter. For example, if the frequency of a low-pass filter response were divided by f_{co} then the resulting response would be “normalized” to f_{co}. A typical normalized low-pass response is shown in Figure 2. The normalized response allows the design engineer to quickly specify the filter needed to meet his system requirements. For example, considering the low-pass filter, the upper frequency range of the pass-band is equal to 0.9 times the cut-off frequency. If the pass-band requirement is DC to 225 MHz then f_{co}, equals 250 MHz. Similarly the stop-band frequencies can be calculated.

## VSWR

A measure of the impedance looking into one port of the filter while the other filter port is terminated in its characteristic impedance, namely, 50Ω. Many times, the impedance match is expressed in terms of return loss. **The conversion between return loss and VSWR is easily attainable using the chart given in Section 0. Most of the filter models shown in this handbook** are designed to present a good impedance match in the pass-band and a highly reflective impedance match in the stop-band. Typically the VSWR in the center of the pass-band is better than 1.2:1 and the VSWR in the stop-band is typically 18:1, very highly reflective. One very notable exception to this VSWR characteristic is the constant impedance band-pass filter series. In these models, both filter ports present a good impedance match in the pass-band and stop-band. **Return loss data over the entire frequency range is given in the CAPD pages. **

## Center frequency

The frequency at which band-pass filters are geometrically centered. For example, if f1 and f2 represent the 3 dB frequency points of a band-pass filter, then the center frequency f0, is calculated as follows:

When the bandwidth, f2 – f1, is a small percentage of the value of f0, then f0, the geometric mean between f2 and f1, will approximately equal the arithmetic mean between f2 and f1.

## Linear phase or flat time delay

Filters have the characteristic of enabling the signal at the filter output to have a constant phase difference for each fixed increment of frequency difference of the signal. Thus:

Where K is a constant.

Mini-Circuits’ PBLP filter models utilize a Bessel-Thomson design to achieve the linear phase characteristic or flat time delay. This enables the transmission of various frequency components contained in a pulse waveform to be delayed by the same amount while traveling through the filter thus preserving the pulse wave shape.

## Group delay

The amount of time it takes for a signal having a finite time duration, such as a pulse, to pass through the filter. Ideally, all frequencies present in the signal should have the same time delay, so that the signal will not be distorted. In most types of filters this is not the case, and group delay defined as dØ/df varies with frequency. For linear phase filters the group delay is constant. It is easy to compare the group delay between a linear phase PBLP low-pass filter and the high selectivity PLP low-pass filters given in the specifications. Referring to the data pages it is observed that the linear phase filters have a much lower and flatter value of group delay.

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