Home Networking Basis: Transmission Environments and Wired/Wireless Protocols

Splitters are used at coaxial cable branch points where the even distribution of power and impedance match are both important. There are power splitters with a different number of output ports. However, all power splitters are built upon the basic one-to-two power splitter component. A one-to-four power splitter/combiner is made by cascading three one-to-two power splitters together (Figure 3.3). Inside a one-to-four power splitter, output ports of the first one-to-two splitter are connected to input ports of two other one-to-two splitters resulting in a total of four external output ports. Using this cascading method, the signal can be evenly distributed among a number of output ports while maintaining impedance matching at all ports.

The one-to-two splitter consists of a center-tapped impedance match transformer and a lumped element power splitter as shown in Figure 3.4. A splitter is used to serve two purposes. The first is for the impedance matching of all cables, and the second is for the isolation between two output ports. The normal impedance of a coaxial cable is 75 ohms. The primary coil with an intermediate tap on the left side of Figure 3.4 serves as an impedance-matching mechanism while generating an electromagnetic field for energy transfer to the second coil. The impedance of each half of the second coil along with attached coaxial cable appears in parallel to the primary coil. The resistor across two ends of the second coil is used to introduce an out-of-phase signal to cancel magnetic coupling between two output ports. The capacitor is used to fine-tune the frequency response of the splitter across the broad range of the frequency band. Because the operating frequency is very high, the detailed component layout inside a splitter could also influence the frequency response.

To study the interaction between coaxial cables and splitters, the ABCD parameters of a splitter from the input port to one output port can be derived. We connect an impedance Z₀ to one output port and treat the input port and the remaining output port as a two-port network. The ABCD parameters for this two-port network are described by Equations 3.7 and 3.8. Corresponding to the structure of a splitter, Equation 3.7 has three parts. The first part represents the primary coil; the second part, the capacitance; and the third part, the second coil together with the resistor. Equation 3.8 shows details of the third part.

Equation 3.7

Equation 3.8

a is the tapping ratio, k₁ is the coupling coefficient of the primary coil, and k₂ is the coupling coefficient of the second coil. L₁ is the inductance of the primary coil, L₂ is the inductance of the second coil, C is the capacitance, and R is the resistance. Typical parameters are listed as follows. We have a = 0.707 for impedance match of 75 to 37.75 ohms,L₁ = 40 mH, L₂ = 0.1 mH, k₁ = 0.9997, k₂ = 0.9997, C = 4.5 pF, and R = 220 ohms. Figure 3.5 shows the frequency responses of a splitter from the input port to one output port with the other output port either terminated with a resistor of 75 ohms or not terminated.

With both output ports terminated with coaxial cables of 75 ohms, the splitter produces a signal-splitting loss of about 3 dB across a broad frequency range of up to the design specification of 500 MHz for this special case. This is the expected result because 3 dB corresponds to half of the energy split. When only one output port is connected, the loss values could vary along the frequency band.

The ABCD parameters from one output port to the other output port are

Equation 3.9

Equation 3.10

Equation 3.11

Equation 3.12

where Z_m = a²Z₁ and Z₁ is the impedance connected at the input port. Figure 3.6 shows the transfer function of a typical one-to-two splitter from an output port to the other output port with the input port either terminated by a coaxial cable of impedance 75 ohms or open. Losses between two output ports are about 25 dB when the input port is connected with a coaxial cable and very high when the input port is open.