Name:Roll no:EXTC-D

Department of Electronics &Telecommunication Engineering

Advanced Communication Lab

Subject: Radio Frequency Circuit Design

Experiment No. 1

Aim:

RF behavior of Passive components and high frequency resistor.

Objective:

To learn introduction to behavior of Passive components and high frequency resistor

Introduction to Radio Frequency:

Radio frequency (RF) engineering is a subset of electrical engineering that deals with

devices that are designed to operate in the Radio Frequency spectrum.

These devices operate within the range of about 3 KHz up to 300 GHz

An RF module is a small electronic circuit used to transmit and/or receive radio signals on

one of a number of carrier frequencies. RF modules are widely used in electronic design

owing to the difficulty of designing radio circuitry

RF engineering is incorporated into almost everything that transmits or receives a radio

wave, which includes, but is not limited to, Mobile Phones, Radios, Wi-Fi, and two-way

radios.

RF engineering is a highly specialized field falling typically in one of two areas;

1. Providing or controlling coverage with some kind of antenna/transmission system

and

2. Generating or receiving signals to or from that transmission system to other

communications electronics or controls.

1

SVKM’S NMIMS

Mukesh Patel School of Technology Management & Engineering

Name:Roll no:EXTC-D

To produce quality results, an in-depth knowledge of mathematics, physics,

general electronics theory as well as specialized training in areas such as wave

propagation, impedance transformations, filters, micro strip circuit board design, etc.

may be required.

Importance of radio frequency design:

Wireless communications (explosive growth of cell phones)

Global positioning systems (GPS)

Computer engineering (bus systems, CPU, peripherals exceeding 600 MHz)

Wire:

Wire in an RF circuit can take many forms.

Wire wound resisters, inductors, and axial-and radial-leaded capacitors all use a wire of

some size and length either in their leads, or in the actual body of the components, or both.

Wire is also used in many interconnect applications in the lower RF spectrum.

The behavior of a wire in the RF spectrum depends to a large extent on the wire’s diameter

and length.

To standardize the size of wire, the American Wire Gauge (AWG) System Commonly used

in the United States.

In American Wire Gauge (AWG) System the size of wire is measured in mil.

1 mil = 2.54X 10-5 m = 0.001 inch

In the AWG (American Wire Gauge) Systems, the diameter of a wire roughly doubles every

six wire gauges.

Example 1:

Given that the diameter of AWG 50 wire in 1.0 mil (0.001inch),

What is the diameter of AWG 14 wire?

2

Name:Roll no:EXTC-DSkin Effect:

A conductor, at low frequencies, utilizes its entire cross-sectional area as a transport

medium for charge carriers.

As the frequency is increased, an increased magnetic field at the center of the conductor

presents impedance to the charge carriers, thus decreasing the current density at the

center of the conductor and increasing the current density around its perimeter.

This increased current density near the edge of the conductor is known as “Skin Effect”.

It occurs in all conductors including resistor leads, capacitor leads, and inductor leads.

The depth into the conductor at which the charge-carrier current density falls to 37% of its

value along the surface, is known as the skin depth and is a function the frequency and the

permeability and conductivity of the medium.

Thus, different conductors, such as Silver, Aluminum, and Copper, all have different skin

depths.

The attenuation constant for the conducting medium is give as

α=√ π f μσ

Therefore the skin depth for the conducting medium is given as

δ= 1α

= 1√ π f μσ

The net result of skin effect is an effective decrease in the cross-sectional area of the

conductor and, therefore, a net increase in the AC resistance of the wire.

For copper, the skin depth is approximately 0.85 cm at 60 Hz and 0.007 cm at 1 MHz Or, to

state it another way : 63% of the RF current flowing in a copper wire will flow within a

distance of 0.007 cm of outer edge of the wire.

3

Name:Roll no:EXTC-D

Straight-Wire inductors

In the medium surrounding any current-carrying conductor, these exists a magnetic field.

If the current in the conductor is an alternative expanding and contracting and, thus,

producing a voltage on the wire which oppose any charge in current flow.

This opposition to change is called self-inductance and we call anything that possesses this

quality as an inductor.

The inductance of a straight wire depends on both its length and diameter

Where

Example 2:

Find the inductance of 5 cm of NO. 24 copper wire with its diameter of 25.3 mils.

The concept of inductance is important because any and all conductors at radio

frequencies (including hookup wire, capacitor leads, etc.) tend to exhibit the property of

inductance.

4

A1=Area of InnerConductor=π r12

A2=Area of Outer Conductor=π r22

Areaof skindepth=A2−A1

¿ π ( r2−r1 )2

Name:Roll no:EXTC-DHigh Frequency Resistors

Resistance is the property of a material that determines the rate at which electrical energy

is connected into heat energy for a given electric current.

The equivalent circuit of a resistor at radio frequencies is given as

Where

“R” is the resistor value. “L” is the lead inductance. “C” is a combination of parasitic capacitance which varies from resistor

to resistor depending on the resistor’s structure.

Carbon-composition resistors

Carbon-composition resistors are notoriously poor high-frequency performance. A carbon-

composition resistor consists of densely packed dielectric particulates or carbon granules.

Between each pair of carbon granules is a very small parasitic capacitor. These parasites,

in aggregate, are not insignificant, however, and are the major component of the device’s

equivalent circuit.

Wire wound resistors

Wire wound resistors have problems at radio frequencies too. As may be expected, these

resistors tend to exhibit widely varying impedances over various frequencies.

This is particularly true of the low resistance values in the frequency range of 10 MHz to

200 MHz. The inductor L, shown in the equivalent circuit is much larger for a wire wound

resistor then for a carbon-composition resistor.

Wire wound resistors look like inductors their impedances will first increase as the

frequency increases. At some frequency (Fr), however, the inductance (L) will resonate

5

Name:Roll no:EXTC-Dwith the shunt capacitance (C), producing an impedance peak. Any further increase in

frequency will cause the resistor’s impedance to decrease as shown

A metal-film resistor

A metal-film resistor seems to exhibit the best characteristics over frequency. Its equivalent

circuit is the same as the carbon-composition and wire wound resistor, but the values of the

individual parasitic elements in the equivalent circuit decrease.

The impedance of a metal-film resistor tends to decrease with frequency above about 10

MHz. This is due to the shunt capacitance in the equivalent circuit.

At very high frequencies, and which low-value resistors (under 50Ω), lead inductance and

skin effect may become noticeable.

The lead inductance produces a resonance peak, as shown for the 5Ω resistance and skin

effect decrease the slop of the curve as if falls off with frequency.

6

Name:Roll no:EXTC-DExample3:

In Fig (Resistor equivalent circuit). The lead lengths on the resistor are 1.27 cm (0.5 inch),

and are made up of AWG14 wire. The total stray shunt capacitance is 0.3 pF. If the resistor

value is 10,000 ohms, what is its equivalent RF impedance at 200 MHz?

RF behavior of Carbon Composition Resistors:

Matlab Code:

clc;close all;c=2e-12;r=2000;l=7;mil=2.54e-3;d=64*mil;L=0.002e-6*l*([2.3*log(4*l/d)]-.75);f=1e6:10e6:500e6;XL=2*pi*f*L*iXC=-i./(2*pi*f*c);Z=(r+2*XL).*(XC)./(r+2*XL+XC);plot(f,abs(Z));xlabel('frequency in MHz');ylabel('Zeq in ohm');title('RF Behaviour of Carbon Composition Resistor')

Output:

7

Name:Roll no:EXTC-D

RF Impedance Behavior of Metal Film Resistors:

1. Plot the Impedance behavior of metal film of 500 Ω resistor with 2.5 cm copper

connections of AWG 26 and a stray capacitance of 5 pF as shown below.

Plot the response using MATLAB Code. Given σ CU=64.516 X 106Ω−1/m

8

Name:Roll no:EXTC-DRF behavior of Metal-film Resistors:

Matlab Code:

Output:

9

Name:Roll no:EXTC-D

Conclusion:

Hence we have studied the RF behavior of carbon composition and metal film resistors and

observed the output for the same.

10