Javalab [Javalab] Lars Drud Nielsen
ldn@oersted.dtu.dk

Ladder network

The circuit is a 3-step resistive ladder (series/shunt) network with a load resistor terminating at the right end. (The circuit might be generalized from 3 steps to N steps.)

Exercise: Let all series resistances have a common value R. Let all shunt (parallel) resistances have a common value q·R (q > 0). Determine a "matched" load resistance RL = x·R that makes the composite resistance seen towards the right from any of the nodes (i.e. the ratio between the node voltage and the rightwards current from the node) equal to RL. Find a general relation between x and q. Also observe that all voltages and currents in the matched case are attenuated by a common factor for each step in the network.

Examples: The applet opens with a matched case, q = 2, x = 2, leading to a step attenuation factor of ½. This case corresponds to the R-2R ladder network utilized in many D/A converters. Try to construct other uniform ladders with matched loads, including cases with very small or very large q values. Wonder about the matched load (the x value) in the latter limit!

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