Transmission lines

## Introduction

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In circuit design connections must be made between components in a design. Typically a metal interconnect is used for these connections. At DC and frequencies well below the microwave range often we assume that the connection is a short circuit between the connected components. A more sophisticated model may include the resistance in the wire. This assumption, for the most part, works well at lower frequencies.

Problems with this assumption start to appear as the wavelength of signals passed through the interconnecting metal approach the dimensions of the interconnecting metal. Imagine that the length of the interconnect is exactly half the wavelength of the signal transmitted through the interconnect. At any given instant in time the signal on each end is exactly opposite the signal on the other end of the interconnect. Clearly the assumption that the interconnect is a short or simple resistance no longer applies in this case. In fact, transmission line effects, or variations from the ideal short, can be seen at much lower frequencies and they significantly impact the way we design circuits at RF frequencies.

## Types of Transmission Lines

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So what exactly is a transmission line? Anything that transmits an electrical signal is a transmission line, even if the transmission line terminates in an open circuit. In practice, there are some common physical types of transmission lines used in RF designs. There are three main categories of transmission lines: planar, waveguide, and wires.

### Planar Transmission Lines

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Planar transmission lines are commonly used in RF circuits due to the ease of manufacturing, lower cost, well understood electrical behavior, the availability of EDA tools for design, and smaller space requirements, among other design benefits. The chief characteristic of planar transmission lines is that the lines are generally routed in two dimensions, as opposed to most waveguide structures which are three dimensional in nature.

Typically, planar transmission lines are metal lines routed on a substrate material such as a printed circuit board, microwave monolithic integrated circuit (MMIC), etc. A ground plane (continuous metal sheet used as a circuit reference) is commonly located close to transmission lines, either on the opposite side of the substrate(i.e. microstrip), on both sides of the substrate (stripline), or above the substrate.

#### Stripline

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Stripline are routed in the middle of a substrate layer between two ground planes. Manufacturing is slightly more difficult than microstrip, though it is still commonly used. Stripline has the advantage of operating in a true TEM mode, as opposed to the quasi-TEM mode of microstrip, which eliminates the frequency dispersion.

#### Slotline

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Slotlines are cuts in a metal plane...

#### Coplanar Waveguide

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#### Coupled Lines

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#### Differential Pair

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#### Shielding

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### Waveguides

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[[Category:[insert category]

#### Rectangular Waveguide

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#### Circular Waveguide

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#### Ridge Waveguide

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#### Fin Line

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### Wires

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#### Coaxial

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#### Triaxial

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#### Twinline

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#### Twisted Pair

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## Signal Propagation

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### TEM Mode

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when the electric and magnetic field of the wave is zero in the direction of propagation is called TEM mode

### TE Mode

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transverse electric mode where the electric field is zero in the direction of propagation and magnetic field has the component in propagation is called TE mode TEM wave can not exit in wave guide(WG)

### TM Mode

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## Transmission Line Modeling

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### Distributed Elements

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### Characteristic Impedence

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### Two Port Model

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Two port network is an electrical circuit with two pairs of terminals. It doesn't mean that two terminals constitute a port. But to form a port a minium of two terminals is required. A grogteruiwphyuiryeuiowyturioeytuioreup of terminals that forms input and/or output connections for a circuit is considered a port.

### Smith Chart

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An open source chart, used commonly for impedance matching application like single and double stub matching.

### Lossy vs. Lossless

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### Discontinuities

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### Frequency Dispersion

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## Transmission Line Circuit Elements

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### Parallel Stubs

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#### Open Circuit Stubs

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#### Short Circuit Stubs

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### Series Stubs

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#### Open Circuit Stubs

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#### Short Circuit Stubs

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## EM Analysis of Transmission Lines

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