radio frequency electronicss-iihr64.iihr.uiowa.edu/myweb/teaching/ece_55195_2015/lectures/l… ·...

A. Kruger 1Radio Frequency Electronics The University of Iowa

Radio Frequency Electronics

Image from Wikipedia

• Born in Council Bluffs, Iowa in 1873• Had 180 patents• Invented the vacuum tube that allows for

building electronic amplifiers• Vacuum tube started electronics age• Patented Phonofilm, an improved method of

adding a soundtrack to movies• Transmitted first radio add• Transmitted first radio report on Presidential

election• Supposedly said: “I came, I saw, I invented—

it's that simple—no need to sit and think—it's all in your imagination.”

• Born in Council Bluffs, Iowa in 1873• Had 180 patents• Invented the vacuum tube that allows for

building electronic amplifiers• Vacuum tube started electronics age• Patented Phonofilm, an improved method of

adding a soundtrack to movies• Transmitted first radio add• Transmitted first radio report on Presidential

election• Supposedly said: “I came, I saw, I invented—

it's that simple—no need to sit and think—it's all in your imagination.”

Preliminaries III

Lee de Forest


Litz WireDue to the skin and proximity effects, current in ac circuits flows near the surface of the conductor. This increases the ac resistance of the conductor.

Due to the skin and proximity effects, current in ac circuits flows near the surface of the conductor. This increases the ac resistance of the conductor.

Images from Wikipedia

Eight strands of insolated wire bundled together.Eight strands of insolated wire bundled together.

To mitigate these effects, one can increase the surface area by bundling many small-diameter strands that are insulated from each other.

To mitigate these effects, one can increase the surface area by bundling many small-diameter strands that are insulated from each other.

Litz wire find application in high frequency inductors and transformers, inverters, communication equipment, ultrasonic equipment, sonar equipment, television and radio equipment and induction heating equipment.

Litz wire find application in high frequency inductors and transformers, inverters, communication equipment, ultrasonic equipment, sonar equipment, television and radio equipment and induction heating equipment.

“Litz” is derived from the German word “Litzendraht” meaning woven wire. “Litz” is derived from the German word “Litzendraht” meaning woven wire.

In transformers and inductors the proximity effect ma dominate.In transformers and inductors the proximity effect ma dominate.

The weaving patterns are designed to ensure the current in is all strands are equal.The weaving patterns are designed to ensure the current in is all strands are equal.


Litz WireIn RF work, Litz wire is used up to 1-3 MHz or so. It is used for RFC, inductors, and ferrite antennas.In RF work, Litz wire is used up to 1-3 MHz or so. It is used for RFC, inductors, and ferrite antennas.

RFC from a vintage radio. The wire is almost certainly litz.RFC from a vintage radio. The wire is almost certainly litz.

Portable radios use litz wire for LW and MW antennasPortable radios use litz wire for LW and MW antennas

0.5 H Inductor from DigikeyCatalog. SRF = 52 kHz.0.5 H Inductor from DigikeyCatalog. SRF = 52 kHz.


Litz Wire ApplicationsFerrite rod antenna with two windings. The main winding resonates will a tunic capacitor. Litz wire is used to reduce coils’ ac resistance.

Ferrite rod antenna with two windings. The main winding resonates will a tunic capacitor. Litz wire is used to reduce coils’ ac resistance.

The main and coupled winding acts as a transformer an can improve impedance matching with the first RF stage.

The main and coupled winding acts as a transformer an can improve impedance matching with the first RF stage.

Image from Wikipedia

Ferrite rod antenna with litz wire windings for LW (< 300 kHz) and MF (535 kHz to 1705 kHz) receptionFerrite rod antenna with litz wire windings for LW (< 300 kHz) and MF (535 kHz to 1705 kHz) reception


Inductor Quality Factor

An ideal inductor has no resistance (or capacitance), only inductance.An ideal inductor has no resistance (or capacitance), only inductance.

A metric for how “good” an actual inductor is, is the so-called quality factor . A metric for how “good” an actual inductor is, is the so-called quality factor .

The quality factor is also used for capacitors and filters, and we will be using it extensively through the course.The quality factor is also used for capacitors and filters, and we will be using it extensively through the course.

It is defined asIt is defined as 2peakenerystoredpercycleenergydissipatedpercycle2peakenerystoredpercycleenergydissipatedpercycle

Assuming sin , the peak energy stored is Assuming sin , the peak energy stored is

Energy dissipated/cycle is:Energy dissipated/cycle is:2

22

222

22

22

1212

2peakenerystoredpercycleenergydissipatedpercycle2peakenerystoredpercycleenergydissipatedpercycle 2

12

1 222

12

1 22


Inductor Quality Factor

2peakenerystoredpercycleenergydissipatedpercycle2peakenerystoredpercycleenergydissipatedpercycle

ReactanceSeriesResistance


Note that Note that

This is also true for a capacitor with a series resistance:This is also true for a capacitor with a series resistance:



1⁄1⁄

1⁄1⁄ 11

Thus, we can writeThus, we can write XXwhere “s” indicates a series connectionwhere “s” indicates a series connection

One can show for the case where a resistor is in parallel with a reactance thenOne can show for the case where a resistor is in parallel with a reactance then

inductor inductor 1⁄ capacitor1⁄ capacitor


Inductors Specifications

Simplified model at a specific frequency . (or is the “component que” Simplified model at a specific frequency . (or is the “component que”

For inductors that are used in signal processing (i.e., filters), the indcutor iductance and a number, the inductor , is normally specified along with the inductance. From this one can determine . For inductors is assumes to be unless otherwise noted.

For inductors that are used in signal processing (i.e., filters), the indcutor iductance and a number, the inductor , is normally specified along with the inductance. From this one can determine . For inductors is assumes to be unless otherwise noted.

s “series”s “series”

Often, (i.e., the resistance at dc) is also specified. This is typically lower than the obtained from – Why?

Often, (i.e., the resistance at dc) is also specified. This is typically lower than the obtained from – Why?

Data sheets often assume the following modelData sheets often assume the following model


Inductor Specifications

10 mH adjustable inductor10 mH adjustable inductor

at the specified frequencyat the specified frequency

Note that the manufacturer did not specify or SRFNote that the manufacturer did not specify or SRF


LR Series LR Parallel TransformationIt is often convenient to work with a parallel network rather than a series network and there exists transformations between the two representations. It is often convenient to work with a parallel network rather than a series network and there exists transformations between the two representations.

1

11

1

Also sinceAlso since2 peakenerystored

energydissipatedpercycle it follows from conservation of energy thatit follows from conservation of energy that

If the component is large then 1 , so one can simplify as follows: If the component is large then 1 , so one can simplify as follows:


LR Series LR Parallel Transformation

Parallel networkParallel network

Series networkSeries network

For the real parts must be equal and the imaginary parts must be equalFor the real parts must be equal and the imaginary parts must be equal

1 1

⇒1 1

Equate real partsEquate real parts

Equate imaginary partsEquate imaginary parts

where

Where do such transformations come from? Below we derive the inverse of the series parallelWhere do such transformations come from? Below we derive the inverse of the series parallel


ExampleExample. Compute the of a 50 nH inductor with series resistance 10Ω at 100MHz.Transform the circuit to an equivalent parallel network.Example. Compute the of a 50 nH inductor with series resistance 10Ω at 100MHz.Transform the circuit to an equivalent parallel network.

1 1 3.14 10 1,08.7Ω

150 10

1 3.143.14 55.1nH

Solution. The of the inductor is Solution. The of the inductor is

2 100 10 50 1010 3.14

Since is low, we will not use the approximation . RatherSince is low, we will not use the approximation . Rather


Capacitors

= permittivity of free space= permittivity of free space

Graphic from Wikipedia

= relative permittivity= relative permittivity

8.85 10 F/m8.85 10 F/m


Capacitor

Assuming the capacitance is known, we use the following equations for circuit analysis.Assuming the capacitance is known, we use the following equations for circuit analysis.

1212

1⁄1⁄

1⁄1⁄

Time domain. Differential equationTime domain. Differential equation

Energy (Joule)Energy (Joule)

Frequency/phasor domain (steady state sinusoidal). Reactance (Ω) Frequency/phasor domain (steady state sinusoidal). Reactance (Ω)

s-domain s-domain

∠ 90°∠ 90° Frequency/phasor domain (steady state sinusoidal). lags by 90°Frequency/phasor domain (steady state sinusoidal). lags by 90°

1⁄1⁄ Time constant for a single time constant circuit, reactive elementTime constant for a single time constant circuit, reactive element


Capacitors

Graphic from Wikipedia


Capacitor Models

The Equivalent Series Resistance (ESR) is, strictly-speaking the equivalent series resistance at a specific frequency, but in practice people use the term as if it is frequency-independent

The Equivalent Series Resistance (ESR) is, strictly-speaking the equivalent series resistance at a specific frequency, but in practice people use the term as if it is frequency-independent


Capacitor Frequency Response

Above ~ 20 MHz, this “capacitor” behaves as an inductor

Above ~ 20 MHz, this “capacitor” behaves as an inductor

Self Resonance Frequency (SRF)Self Resonance Frequency (SRF)


Decoupling Capacitors… and here?… and here?

What is going on here…What is going on here…

Question: Why place a 100 nF capacitor in parallel with a 100 F capacitor?Question: Why place a 100 nF capacitor in parallel with a 100 F capacitor?

Answer: The 100 F will begin to behave like an inductor as some frequency. At this frequency the 100 nF “takes over” and ensure low reactance.Answer: The 100 F will begin to behave like an inductor as some frequency. At this frequency the 100 nF “takes over” and ensure low reactance.


Build a Good Capacitor

It is very common in RF and high-speed digital work to place a number of capacitors in parallel so that the composite capacitor has a low reactance where desired.It is very common in RF and high-speed digital work to place a number of capacitors in parallel so that the composite capacitor has a low reactance where desired.

One should carefully consider package sizes, since that determines inductance

One should carefully consider package sizes, since that determines inductance

Graphic from Planet Analog


De-queingDe-queing

http://www.planetanalog.com/showArticle.jhtml?articleID=200001206


Ceramic Capacitor Construction

Dipped ceramic capacitors are cut from large sheets of “green” ceramic material and fired. Electrodes are screen printed using silver, finely powdered glass, and a binder on both sides of the disk, then back to the oven. This evaporates the binder, and the melted glass binds the silver to the ceramic surface.

Dipped ceramic capacitors are cut from large sheets of “green” ceramic material and fired. Electrodes are screen printed using silver, finely powdered glass, and a binder on both sides of the disk, then back to the oven. This evaporates the binder, and the melted glass binds the silver to the ceramic surface.

Next, hairpin wires are clipped onto the capacitor and it is dipped in solder.

These capacitors are inexpensive and available in values less that ~ 1 µF.

Next, hairpin wires are clipped onto the capacitor and it is dipped in solder.

These capacitors are inexpensive and available in values less that ~ 1 µF.

These capacitors are inexpensive and available in values less that ~ 1 µF. These capacitors are inexpensive and available in values less that ~ 1 µF.


Monolithic/Multilayer Ceramic Capacitors

The base ceramic material is mixed with a binder and fashioned into sheets. Electrodes are painted onto one side of the sheets using a paint that consists of a liquid binder with fine metal particles in suspension.

The base ceramic material is mixed with a binder and fashioned into sheets. Electrodes are painted onto one side of the sheets using a paint that consists of a liquid binder with fine metal particles in suspension.

A Surface Mount (SMT) MLC capacitor.A Surface Mount (SMT) MLC capacitor.

The sheets are stacked on top of each other. The painted electrodes are arranged so that alternate electrodes exit from opposite ends. The laminated layers are then compressed and fired, which sinters them into one monolithic structure.

The sheets are stacked on top of each other. The painted electrodes are arranged so that alternate electrodes exit from opposite ends. The laminated layers are then compressed and fired, which sinters them into one monolithic structure.

The ends are terminated, often using silver. For leaded capacitors, wires are attached, and finally the capacitor is encapsulated in plastic and markedThe ends are terminated, often using silver. For leaded capacitors, wires are attached, and finally the capacitor is encapsulated in plastic and marked


Capacitor Quality Factor

2peakenerystoredpercycleenergydissipatedpercycle2peakenerystoredpercycleenergydissipatedpercycleRecall the definition of the component Recall the definition of the component

XX“s” series“s” series

1⁄ capacitor1⁄ capacitor

1⁄1⁄

“p” parallel“p” parallel


RC Parallel Series RC Transformations

1⁄1⁄ 1

11 1

1 1

1

1

Parallel networkParallel network

Series networkSeries network

For the real parts must be equal and the imaginary parts must be equalFor the real parts must be equal and the imaginary parts must be equal

11 ⇒

1 1

With the of the parallel network, the expressions becomeWith the of the parallel network, the expressions become

11


Capacitor Terminology

)()()( jXRjZ

cos

powerapparent losspower

2

2

ZR

ZIRIPF

tancot

storedpower reactivelosspower

2

2

XR

XIRIDF

13.0tan 41.7

Power Factor (PF) and Dissipation Factor (DF) Real capacitors have both resistive and reactive components (see the model for the capacitor)Power Factor (PF) and Dissipation Factor (DF) Real capacitors have both resistive and reactive components (see the model for the capacitor)

DF is normally expressed as a percentage. For example, if the DF of a capacitor is 13%, then: DF is normally expressed as a percentage. For example, if the DF of a capacitor is 13%, then:

radio frequency electronicss-iihr64.iihr.uiowa.edu/myweb/teaching/ece_55195_2015/lectures/l… ·...

Documents