Smith Chart Flashcards by chxngy Unknown

One of the most useful graphical tools for high frequency circuit applications

Smith Chart

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Smith Chart is one of the most useful graphical tools for

High frequency circuit application

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The Smith chart provides a clever way to ________ and it continues to endure popularity decades after its original conception.

Visualize complex functions

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From a mathematical point of view, the Smith chart is simply a presentation of ________ with respect to coordinates defined by the reflection coefficient or it can be defined mathematically as one port scattering parameter

all possible complex impedances

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A Smith chart is a ______ with a lot of interlaced circles on it;

Circular plot

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Who invented the Smith Chart?

Phillip Hagar Smith

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While working for _____, Phillip Hagar Smith invented his eponymous Smith chart

RCA

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When did Phillip Hagar Smith retired from Bell Labs?

1970

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Smith Chart was primarily developed, extended, and refined by Phillip Hagar Smith, in a series of published works between _______

1939 and 1969

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Wave that remains stationary, fromed by the interference of two waves traveling in opposite directions

Standing wave

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KEy characteristics of Standing Wave

Nodes, Antinodes, Formation

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Applications of Standing Wave

Musical Instruments, Physics & Engineering

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Points of zero amplitude

Nodes

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Points of maximum amplitude

Antinodes

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Occurs in confined mediums (e.g., strings, air columns)

Formation

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Ratio of reflected power to incident power in a waveguide and is equal to the square of the voltage reflection coefficient but without phase

Power reflection coefficient

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In a lossless waveguide, it (1) ______, while in an attenuating waveguide, it (2) ________

(1) remains constant
(2) decreases toward the generator

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When expressed in dB, it is known as ________

Return loss

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As voltage and current waves travel toward the load in a waveguide, some power is lost due to _____________

Conductor resistance and dielectric leakage

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The power loss due to conductor resistance and dielectric

Attenuation or one-way transmission loss

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When the input impedance Zin, is equal to the charateristic impedance Zc and the load impedance Zl. There are __________ and _________ will not change the input impedance of the line

No standing waves and changing the frequency of the generator

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There is a maximum possible power transmitted to the load, and the line is said to be ________

Flat or nonresonant

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If impedance of load ZL is not equal to the characteristic impedance, the line may

Appear parallel or resonant circuit

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Input impedance of the line will vary as a function of electrical length and therefore of the frequency of the carried signal, the line is said to be ________

Resonant

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When the line is open ended, the input imedance Zin is

Minimum for odd multiple of λ/4

When the line is open ended, the input impedance Zin is

Maximum for even multiple of λ/4

When the line is open ended, the input impedance Zin is _______ after the first even multiple, and before the first odd, so on.

Capacitive (R - JXc)

When the line is open ended, the input impedance Zin is ______, after the first odd multiple, and before the even multiple and so on

Inductive (R+JXI)

When the line is short ended, the input impedance Zin is

Maximum for odd multiple of λ/4

When the line is short ended, the input impedance Zin is

Minimum for even multiple of λ/4

When the line is short ended, the input impedance Zin is ________, after the first even multiple and before the first odd, so on.

Inductive (R+JXc)

When the line is short ended, the input impedance Zin is ________, after the first odd multiple and before the even multiple, so on.

Capacitive (R-JXI)

Parameters plotted in Smith Chart

Reflection Coefficient Magnitude Reflection coefficient phase angle Length of transmission line between any two points in wavelength VSWR Input Impedance Zin The location of Vmax and Vmin

General Formula of Impedance

Z = R +- jX Where: R = the real part (resistance) X = the imaginary part (reactance)

Another normalized impedance Formula

Zn = Za / Zo Where: Zn = The normalized impedance Za = The actual impedance Zo = The characteristic impedance

General formula of Admittance

Y = G + jB Where: G = the real part (conductance B = the imaginary part (susceptance)

The reciprocal of the impedance Z formula

Y = 1/Z

Conductance (G) formula:

G = R / (R^2 + X^2) Where: R = real parts of the normalized impedance X = imaginary parts of the normalized impedance

Susceptance (B) formula

B = -X / (R^2 + X^2)

The upper half of the Smith chart represents what?

Inductive reactance

The _____ of the Smith chart represents inductive reactance

Upper half

As you move upwards on the chart, the imaginary part of the impedance ____________, which corresponds to inductive behavior

Increases in the positive direction

The lower half represents _______

Capacitive reactance

The ________ represents capacitive reactance

Lower half

As you move downwards, the imaginary part of the impedance _____________, which corresponds to capacitive behavior

Becomes negative

The dual scale wavelength circle of the Smith Chart can be located _________

Beneath the outer rim

Dual-scale wavelength circle of the smith chart has two scales, what are those?

Outer scale (toward generator) Inner scale (toward load)

The outer scale in the dual-scale wavelength circle is marked

Wavelengths toward generator (that is from the load)

The values of the outer scale increase when moving around the circle in a ____________

Clockwise direction

The inner scale is marked

Wavelengths toward load (that is from the generator)

The valueof the inner scale increase when moving around the circle in a _________

Counterclockwise direction

It shows how much the reflected wave is phase-shifted when bouncing back

Reflection coefficient angle

Formula for reflection coefficient angle

θΓ=∠Γ

It shows how much the signal’s phase changes as it continues through the system

Transmission coefficient angle

Formula for transmission coefficient angle

θΓ=∠(1+Γ)

A _________ is at the center, where there is no reflection, ensuring maximum power transfer with no signal loss

Matched load (ZL = Zo)

A matched load (ZL = Zo) can be found at the what?

At the center of the smith chart

A _________ is located at the far left, where all the signal is reflected with a 180 degrees phase shift and no power is transmitted

Short circuit (ZL = 0)

A short circuit (ZL = 0) is located at the what?

At the far left

An _________ is at the far right, where the signal is also fully reflected but without a phase sift, meaning voltage is maximum and current is zero

Open circuit (ZL = infinity)

An open circuit is located at the what?

At the far right of the Smith Chart

The center of the Smith chart is called what?

The prime center

What does the prime center corresponds to?

To the Zo

In most RF systems, how much load does Zo have?

Purely resistive 50-Ohm Load

The Smith Chart normalizes the ________ to 1

Source impedance

represent a family of circles where all points along a single circle have the same normalized resistance value.

Resistance circles

another set of circles where all points on a single circle have the same normalized reactance value.

Reactance circles

To examine the impedance, first measure the ________

Modulus or magnitude of the reflection coefficient.

Next, locate the _________ coordinate and move left or right along the scale

Center coordinate

The ___________ mark is at the far left and will be used as a reference point

Origin mark

The first ruler top part of the Smith Chart is marked _______. Its value ranges from 1 to infinity

SWR or Standing Wave Ratio

The upper part of the ruler is in (1) ___________ scale, while the lower part shows the (2) _________ scale, which refers to SWR in dB

(1) linear scale (2) dB scale (dBS)

The second ruler (top part) is marked _______. This shows how much of the signal is reflected back

RTN.LOSS, or Return Loss in dB

At the center of the Smith chart, which is a perfect match, there is no reflection, therefore the return loss is _______

Infinite

At the boundary or total reflection, the return loss is ______

0 dB

The lower part of the ruler shows ________ in terms of power. This is proportional to the square of the reflection coefficient

RFL.COEFF. P, or Reflection Coefficient

The third ruler (left) marked as ______ shows the modulus (absolute value) of the reflection coefficient on a linear scale

RFL.COEFF, E or I (voltage or current)

Fourth ruler measures the _______, which ranges from 0 (short circuit) to +2 (open circuit). It’s only valid when the load impedance (ZLoad) is real

Voltage transmission coefficient

The third ruler (right, marked as ________), shows the transmitted power based on the mismatch

TRANSM.COEFF.P

At the center, which is a perfect match, ________ is transmitted

All power

At the boundary (total reflection) ______ is transmitted

No power

The second ruler (right, marked as ________), shows the reflection loss in transmitted wave, not to be confused with return loss (reflected wave). It displays the relationship as Pt = 1 - Γ² in dB

RFL.LOSS in dB

The first ruler (right, marked________), measures the attenuation of a lossy line (like an attenuator) with an open or short circuit termination (full reflection).

ATTEN. in dB

Types of Smith Chart

- Impedance or the Z-Smith chart - Admittance or the Y-Smith chart. - Immittance Smith chart or the YZ chart

Represents the opposition to current flow in a circuit, and is measured in ohms.

Impedance or the Z-Smith Chart

polar graphs that show the normalized line impedance in the complex reflection coefficient plane. It is made of circles that represent different values.

Impedance or the Z-Smith chart

Is the reciprocal of impedance, indicating how easily current can flow through a circuit.

Admittance or the Y-Smith chart

can be obtained by rotating the impedance chart by 180°. The upper half of the chart represents negative values of S (or negative susceptance)

Admittance or the Y-smith chart

Is used when both series and parallel components are present in the circuit. It superimposes the impedance and admittance charts on each other

Immittance Smith chart or the YZ chart

Components of Impedance Smith Chart

Constant R Circle Constant X Circle

Components of Admittance Smith Chart

Constant C circle Constant S circle

The horizontal line represents the resistance axis. It is used to represent the complex impedances of the resistive part of circuit.

Constant R Circles

It is known as the constant reactance circle. The reactance axis lies across the the circumference of the Smith Chart.

Constant X Circles

The admittance chart is just the reverse of the impedance chart. What are these components?

Constant C and S circles

It is a measure of the mismatch between the transmission line and the load, indicating how much of the signal is reflected back due to this mismatc

Standing Wave Ratio (SWR or VSWR)

Reflection Coefficient Formula

r = ZL - Zo / ZL + Zo Where: ZL = load impedance Zo = characteristic impedance r = Reflection coefficient

VSWR Formula

VSWR = 1 + | r | / 1 - | r | Where r = Reflection coefficient