Magicomm Technologies Ltd

 

CATV Diplex Filter

                                                                                                            By Allan Sobryan                                            

 

Introduction

 

 

The age of high-speed data communications and multimedia application have dawned on cable television. It has brought with it a myriad of services such as high-speed data, video on demand, telephony, and Internet to name a few. A cable plant must be two-way ready to carry this high-speed data traffic from a variety of sources.

 

 In a two-way cable television plant, diplex filters have been employed to separate forward and reverse path signals. A diplex filter is a Low-pass and High-pass filter combination. In a cable TV plant, frequency division multiplexing (FDM) format is employed to carry the cable television signals on one cable. High crossover isolation of these diplex filters, keep the forward and return path signals sufficiently separated preventing any loop gain oscillations between the forward and return paths.

 

In a typical CATV trunk amplifier station, a quantity of three diplex filters are used (trunk in, trunk out, and Bridger) and in a line-extender an arrangement of two diplex filters (Input and Output). In North America, a modern diplex filter Low-pass section would pass frequencies between 5 Mhz through 42 Mhz (reverse path) and the High-pass filter section would pass frequencies between 54 Mhz through 860 Mhz (forward path).

 

With cable operators activating their reverse path to accommodate these new services, it is important that electrical parameters of diplex filters with respect to design, frequency response, return loss, insertion loss, roll-off characteristics, crossover isolation, in-band isolation and group delay specifications be understood. It is beyond the scope of this article to provide more than a fundamental understanding and appreciation of diplex filter design, as it applies to CATV. Many good textbooks have been written on filters to satisfy those individuals wanting to explore the development of electrical formulas and to gain a deeper understanding of these circuits. The magic of RF filters lie in the creativity of the RF designer to choose the appropriate layout, shielding, and special components, coupled with the special touch of the alignment technician to create the filter performance necessary for today’s modern system architecture.

 

 

What is a filter?

 

 

The Webster’s dictionary defines the word, filter, as a device for screening out or “separating” certain frequencies. In cable television, a filter is a network comprising of coils and capacitors in a certain configuration that is designed to discriminate between frequencies. Filter networks pass some frequencies and reject others. Our discussion begins with an overview of some basic filter block diagrams. Generally, filters can be classified by their functionality. The classifications are as follows: -

 

 

 

 

·         Low-pass

·         High-pass

 

 

·         Band-pass

·         Band-reject

 

 

Figure 1: Block diagram of a Low-pass filter

 

 

           

            Low-Pass

            Filter
 
 


           

                        INPUT                                                  OUTPUT

 

 

 

 


Figure 2: Ideal Low-pass filter frequency response

                       

                        Amplitude                               

                                          dB  Output

 

                                   

 

 

 

 

 


                              42 Mhz       Frequency

 

 

·          In North America, the Low-pass filter is designed to pass all frequencies below 42 Mhz and to reject all frequencies above 42 Mhz. When this Low-pass filter is connected to a 75 Ohms load, at frequencies below 42 Mhz the input of the filter looks like a resistive impedance of 75 Ohms. We can say that the signal does not see the filter; it is transparent to these signals.

 

·         At frequencies above 42 Mhz, the Low-pass filter rejects or blocks these frequencies from passing through the low pass filter. At these frequencies, the Low-pass filter is no longer resistive in nature but purely reactive.

 

·         From basic circuit theory, no real power enters a reactive load, so at frequencies above 42 Mhz, the filter looks like a mirror and are reflected back towards the source.

 

 

·         The High-pass filter is designed to pass all frequencies above the cut-off frequency. The cut-off frequency is a function of circuit components.

 

·         Band-pass and Band-reject filters perform the functions implied by their names. In the case of the band-pass, one band of frequencies is delivered through the filter to the output and all other frequencies are suppressed. The center and width of the pass-band are determined by the circuit components chosen.

 

·         The Band-reject filter is designed to suppress or reject one band of frequencies and to pass all other frequencies. Untuned and tuned circuit filters can be designed by using combinations of resistors, capacitors and inductors in certain circuit configurations.

 

 

 

Figure 3: Simplified block diagram of a diplex filter arrangement in a CATV amplifier

 

 

 

High Pass

Filter
 

Low Pass

Filter
 

High Pass

Filter

 

 
 
                        Cable                                       Forward AMP

                                    75 W                                                                                     OUTPUT

INPUT

 

 


                                                                       

Low Pass

Filter
 
                                                                        Reverse AMP

                                      j1000 W                                                                          j 1000 W                                                                                                                                                      

 

 

 

 

 

·         Figure 3 shows a simplified block diagram of a cable amplifier with a high pass and low pass filters in parallel. Let us consider what happens to the downstream signals (forward) when they are applied to the input of the forward amplifier.

 

·         The downstream signals (forward) will pass transparently through the high pass filter but rejected by the low pass filter. If the input impedance of the high pass and low pass filters to these frequencies are as shown in diagram 3, then the combined impedance is calculated as follows:

 

 

 

In rectangular form:        Z (input) =     75 X j1000 W                                              eq.        1

                                               

                                                        75 + j 1000 W

 

 

Multiplying by (75 - j 1000)          = (j 75000)(75 - j1000)                                        eq.        2

                                                                       

                                                 (75 + j1000) (75 - j1000)

 

 

Expanding eq. 2             = j 5625000 - 75000000 j2                                               eq.        3

 


                                                (5625 +j75000 - j75000 - 1000000 j2)

 

 


                                                =( j 5625000 - 75000000 j2)                                 eq.        4

 


                                                       (5625 - 1000000 j2)

 

Substituting j2 = -1, we simplify equation 4 to:

 

                                                = j 5625000 + 75000000                                     eq.        5

                                                      (5625 + 1000000)

 

                                                = 75000000 + j 5625000                                     eq.        6

                                                     (1005625)                                                    

                                                           

                       

Input Impedance (series equivalent)=       74.5 + j 5.6 W

                                                           

                                               +j         

Phasor representation                                    

 

 


                                    - x                                       + x

 

 

 


                                                           

                                                         -j

In polar co-ordinates:      Z (input) =          74.8 Š4.2° W

 

 

Smith Chart:

 

 

To avoid calculating the cumbersome mathematics above when dealing with complex impedances, the RF filter designer may use the Smith chart option in a digital RF network analyzer such as in a H/P 8753D to plot the input/output complex impedance/admittance of the filter network. The Smith chart named after its inventor Philip H. Smith consists of a series of overlapping circles, which intersect each other at right angles. The pure resistance line forms the reference for measurements made on the chart and bisects the chart in half. Above and below the reference pure resistance line are constant reactance circles. The circles above the pure resistance line represent inductive reactance and those below represent capacitive reactance.

 

 

 

Figure 4: Block diagram of a High pass filter

 

 

 

 

 


INPUT                                      OUTPUT

 

 

 

 

 

 

 


Figure 5: Ideal High-pass filter frequency response

 

                        Output

                        Amplitude     dB

 

 

 

 

 


                                                             

 


54 MHz                                     Frequency

 

 

Figure 6: Amplitude and phase characteristics of practical LP & HP filters

            LPF                                                                  HPF

            Amplitude                                                        Amplitude

 

 


 

 

 

 


                        Frequency                                                                   Frequency

 

 

            Phase                                                              Phase

 


            +                                                                      +


            _                                                                      _

            Frequency                                                                   Frequency

 

 

·         The output voltage of the low pass filter lags the phase of the input voltage.

 

·         The output of the high pass filter leads the phase of the input. A leading phase angle means that the output voltage reaches the maximum part of its cycle before the input voltage.

 

 

 

Basic filter Configurations:

 

A) “ L” Type

 

 

 

 

 

 

 

 

 


B) “ Õ ” Type

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


(C) “ T ” Type

 

 

 

 


                       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


(D) “ Lattice ” Type

 

 

 

    Z1
 
                          

 

 

 

 

 

 

 

 

 

 

 

 


·         The four basic filter configurations are shown above. Figure A “ L “ type forms the basic building block and forms the foundation for all other filters.

 

·         Figures B, C and D, the “ P “, “ T “, and “ Lattice” types correspond to the relative positions of the network components to each other.

 

In addition to the basic types, you can construct multiple sections to form a compound configuration i.e. double “ L “, double “ P “, and double “ T”. The addition of more sections increases the effectiveness of the filter about its cut-off point; the slope of the response curve becomes steeper.

 

 

Constant K Filter design approach:

 

 

The challenge, which faces a RF filter designer, is to consider layout and shielding in the filter design. Keeping the output and input of the filter physically separated to prevent unwanted coupling of signal energy between them. Attention must be paid that air core inductors are either shielded, placed at right angles or substitute the use of toroidal inductors. Constant–K filters are designed to reject certain frequencies but matches the characteristic impedances between the source and load throughout its pass band. A modified version of the constant-K filter is the m-derived filter. This type of filter exhibits an extremely sharp cutoff, while maintaining a constant impedance throughout its pass band.

 

 

A Low-pass “ L “ type constant K design filter is one in which Z1 Z2 = K2

 

            Where   Z1  = the impedance of the series arm of the filter.

                        Z2 = the impedance of the shunt arm of the filter.

            And

                        K = a constant = Ro characteristic impedance of the filter.

 

 

·         In a Low-pass filter constant -K filter design, the cut-off frequency (-3 dB) is determined by:

                                                  

Fc =                 1                                 

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