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Resistors In Series

Resistors In Series

A resistor is an ohmic device that limits the flow of charge in a circuit. Most circuits have more than one resistor. If several resistors are connected together and connected to a battery, the current supplied by the battery depends on the equivalent resistance of the circuit. The equivalent resistance of a combination of resistors depends on both their individual values and how they are connected. The simplest combination of resistors is the series combination.
In a series circuit, the...

Resistors In Parallel

Resistors In Parallel

Resistors are in parallel when one end of all the resistors are connected to a continuous wire of negligible resistance and the other end of all the resistors are also connected to one another through a continuous wire of negligible resistance. In the case of a parallel configuration, the potential drop across each resistor is the same. Current through each resistor can be found using Ohm’s law, I = V/R, where the voltage is constant across each resistor. The sum of the individual currents...

Equivalent Resistance

Equivalent Resistance

In circuit analysis, situations often arise where resistors are neither in series nor parallel configurations. To tackle such scenarios, three-terminal equivalent networks like the wye (Y) (Figure 1 (a)) or tee (T) and delta (Δ) (Figure 1 (b)) or pi (π) networks come into play. These networks offer versatile solutions and are frequently encountered in various applications, including three-phase electrical systems, electrical filters, and matching networks.

Combination Of Resistors

Combination Of Resistors

Electrical devices in any circuit can be connected either by series or parallel connections. Additionally, circuits can be connected involving both of these connections, known as combination or complex circuits. As these circuits have complex resistor connections, it is necessary to identify different parts as either series or parallel connections, then the whole combination of series and parallel resistors can be reduced to a single equivalent resistance. With the known equivalent resistance...

Design Example: Strain Gauge Bridge or Wheatstone Bridge

Design Example: Strain Gauge Bridge or Wheatstone Bridge

The utilization of strain gauges as transducers for converting mechanical strain into electrical signals is a common practice in various engineering applications. These strain gauges are frequently integrated into Wheatstone bridge circuits to accurately measure parameters such as force or pressure. Within this context, each element within the circuit exhibits a resistance that undergoes subtle variations when subjected to mechanical strain. The primary objective is to convert minuscule...

Voltage Dividers

Voltage Dividers

In electrical circuits, resistors can be connected in series, sequentially linked one after the other. In a series configuration, the same current flows through each resistor. Ohm's law is a fundamental principle to understand the behavior of resistors in series. It expresses the voltage across these resistors in terms of the current and resistance.
Kirchhoff's voltage law implies that the sum of the voltages across the resistors in series equals the source voltage. This means that the current...

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Optimal Series Resistors for On-Wafer Calibrations.

Jasper A Drisko¹, Richard A Chamberlin¹, James C Booth¹

¹National Institute of Standards and Technology, Boulder, CO 80305 USA.

IEEE Transactions on Microwave Theory and Techniques

|June 1, 2026

Summary

This summary is machine-generated.

This study optimized series resistors for on-wafer calibration and transmission line analysis. Near 100 Ω, resistors excel in calibration, while 150 Ω and shorter designs minimize uncertainty in capacitance extraction.

Keywords:

Calibration capacitance microwave on-wafer scattering parameters series resistor

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Area of Science:

Electrical Engineering
Materials Science

Background:

Series resistors are crucial for on-wafer calibration and characterizing coplanar waveguide transmission lines.
Previous research focused on applications, not the optimal design of the series resistor itself.

Purpose of the Study:

To investigate the impact of dc resistance and geometry on series resistor performance.
To determine the optimal series resistor design for on-wafer calibration and capacitance extraction.

Main Methods:

Fabrication of 48 series resistors with varying dc resistances (1 Ω to 6 kΩ).
Evaluation of resistor utility in series-resistor calibration against multiline thru-reflect-line (TRL).
Assessment of capacitance per unit length extraction for coplanar waveguide transmission lines.

Main Results:

A dc resistance near 100 Ω yielded the best performance for series-resistor calibration.
Resistors with dc resistance near 150 Ω and lengths under 20 μm provided the lowest uncertainty in capacitance extraction.
Guidance on selecting appropriate frequency bounds for capacitance estimation was provided.

Conclusions:

The optimal series resistor design is dependent on the specific application (calibration vs. capacitance extraction).
Resistor geometry and dc resistance are critical parameters for on-wafer measurements.
Findings aid engineers in selecting optimal series resistors for improved on-wafer calibration and transmission line analysis.