Resistor ladder networks: A resistor ladder (e.g., R–2R ladder) is a specialized form of series–parallel circuit. True or false?

Introduction / Context:
Resistor ladders appear in digital-to-analog converters (R–2R DACs), voltage dividers with multiple taps, and measuring bridges. They are built from repeating resistor sections and must be recognized as structured combinations of series and parallel connections.

Given Data / Assumptions:

• Resistor ladder: a repeating network of resistors forming a “ladder” pattern.
• Sections combine series and parallel branches.
• Linear, time-invariant resistive elements (no reactance) are assumed.

Concept / Approach:

A series–parallel circuit is any network reducible by successive series and parallel combinations without requiring bridge-network transformations. Most ladder sections meet this criterion: each rung and rail combination reduces to equivalent series/parallel forms, especially in canonical R–2R topologies.

Step-by-Step Solution:

Verification / Alternative check:

Calculate Thevenin equivalents from successive ladder sections: the repeated halving property of R–2R networks emerges from series–parallel reductions, confirming the classification.

Why Other Options Are Wrong:

• Claiming “False” implies ladders cannot be treated by series–parallel methods, which is untrue for standard ladders (though some bridge-configured ladders may require more advanced techniques).

Common Pitfalls:

Confusing a general “ladder” with a “bridge” network. Some resistor networks do form bridges that are not strictly reducible by series/parallel alone. Standard R–2R DAC ladders, however, fit the series–parallel classification.

Final Answer:

True