![]() Note that the 0.5 dB in-band ripple results in a return loss of -10 dB as expected.Ī low pass filter may be converted to a bandpass filter by employing a suitable mapping function. The schematic of the filter, which was derived from Chebyshev, the low pass prototype elements and the associated frequency response are shown in Figure 4. 1, and repeated in Appendix A for convenience. In addition to the tabulated data of low pass prototype filter elements, the values may be computed via execution of the equations found in Matthaei, et al. To construct the filter at another frequency (1.0 GHz, for example) and circuit impedance level (R 0 = 50 W ), the element values must be adjusted (de-normalized) in accordance with If this five-section prototype filter were constructed from available tables of elements and a circuit simulation performed, the transfer function would be exactly as represented in the schematic. The prototype elements are from Matthaei, Young and Jones 1 where the normalized cutoff frequency is given in the radian format w ' 1 = 1.0 = 2 p f' 1. The low pass prototype filter parameters for the low pass Chebyshev filter example areĪ schematic representation of the prototype Chebyshev filter is shown in Figure 3. A graphical representation of the power transfer function of the Chebyshev low pass prototype filter is shown in Figure 2. These equations represent the power transfer function of the Chebyshev low pass prototype filter with normalized filter cutoff frequency f' of 1.0 Hz. The power transfer function of the Chebyshev filter may be represented by To represent an even number of elements of the prototype filter, simply remove the last capacitor or inductor of the ladder network.įor purposes of illustration, an example representing a Chebyshev filter is offered. The illustrated circuit topologies represent a filter prototype containing an odd number of circuit elements. ![]() S = s + j w, the Laplace complex frequency variableĬlearly, the transfer function, T(s), is a polynomial of order n, where n is the number of elements of the low pass filter prototype. In both cases, the network transfer function is This diagram also depicts the two possible implementations of the low pass prototype filter topologies. The elements of the low pass prototype filter are the capacitors and inductors of the ladder networks of the synthesized filter networks as shown in Figure 1. The element values have been normalized with respect to one or more filter design parameters (cutoff frequency, for example) to offer the greatest flexibility, ease of use and tabulation. Low pass prototype filters are lumped element networks that have been synthesized to provide a desired filter transfer function. A number of illustrated examples are offered to validate the design procedure. This article presents a general design procedure for bandpass filters derived from low pass prototype filters, which have been synthesized for a unique filter parameter. The low pass prototype elements are available to the designer in a number of tabulated sources 1,2,3 and are generally given in a normalized format, that is, mathematically related to a parameter of the filter prototype. The low pass prototype elements are the normalized values of the circuit components of a filter that have been synthesized for a unique passband response, and in some cases, a unique out-of-band response. ![]() Of the available techniques for the design of bandpass filters, those techniques based upon the low pass elements of a prototype filter have yielded successful results in a wide range of applications.
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