snvhome.netsnvhome.net/ee-braude/devices-lab/labs/r-c-l... · web viewbraude college of...

R-C-LCharacterization

May 19, 2023

Department of Electrical & Electronic Engineering Braude College of Engineering

Advanced Laboratory for Characterization of Semiconductor Devices - 31820

Dr. Radu Florescu Dr. Vladislav Shteeman

Department of Electrical and Electronic Engineering ORT Braude College


The goal.

The goal of this experiment is to characterize the frequency behavior of 3 passive electronic

components: resistor, coil and capacitor. You will measure the frequency-dependent impedance

Z ( f ) of those components by using Keithley SCS 4200 measurement system and Agilent 4284A C-

R-L analyzer.

The following parameters will be measured:

Resistor impedance ZR as a function of applied frequency

Coil impedance ZL as a function of applied frequency

Capacitor impedance ZC as a function of applied frequency

Dr. Radu Florescu Dr. Vladislav Shteeman 2



Short theoretical background.Usually, electrical engineering deals with the physical model of ideal passive electronic components: resistors, capacitors and inductors (coils):

Ideal resistor[1] is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current passing through it in accordance with Ohm's law: U=IR . It is assumed that ideal resistor has frequency-independent purely real

impedanceZR (f )=R .

Ideal inductor[2] (coil) is a two-terminal electronic component that can store energy in a magnetic field created by the electric current passing through it. A coil's ability to store magnetic energy is measured by its inductance (in units of henries). Typically, an inductor is a conducting wire shaped as a coil, the loops helping to create a strong magnetic field inside the

coil due to Faraday's Law of Induction: |ε|=N|

dΦB

dt|(where |ε| is the magnitude of the

electromotive force (in volts), N is the number of turns of wire and ΦB is the magnetic flux (in webers) through a single loop). It is assumed that coil is a short circuit for DC and has purely

imaginary frequency-dependent impedanceZL (f )=i2 π fL .

Ideal capacitor[3] is a two-terminal electronic component that characterized by a single constant value, capacitance, which is measured in farads. This is the ratio of the electric charge on each

conductor to the potential difference between them:C= q

U . It is assumed that capacitor is a circuit opening for DC and has purely imaginary frequency-dependent impedance

ZC (f )= −i2π fC .


ZReRZR

ZIm



In sum up, for the ideal components, Z is purely real for R, and purely imaginary for C and L. For L,

the phase of Z is rotated by angleπ

2 , while for C, it is rotated by angle −π

2 (see Figure 1).

Figure 1. Impedance of the ideal R, C and L components in the complex plane.

Nevertheless, in any real passive component always present some physical factors (i.e. input-output contacts, interface contacts of different chemical materials inside the component etc), preventing it from functioning as an ideal one. In order to account for these factors and accurately predict the performances of the component under different operation conditions, the concept of equivalent circuits, representing a single real passive element as an array of different ideal passive elements was introduced. Thus, each true passive component has a complex impedance function,Z ( f ) , which can be decomposed onto the real and imaginary parts (active Re ( Z ) , and reactive Im ( Z )parts) (see Figure 2).

Figure 2.Impedance of equivalent circle on the complex plane.

Note that the same element can be represented by a number of equivalent circuits. Different equivalent circles reflect different operation modes of the same component.

Presented below some examples of equivalent circles for R, C and L.


|ZC|=1

2π fC

|ZL|=2π fL

Zalignl¿ equivalent ¿circle ¿¿Im ( Z )

Re ( Z )θ



Equivalent circle and frequency dependence of resistor.

Figure 3. Equivalent circle of resistor (after [6]).

Figure 3 shows equivalent circle of resistor. Notation:

C ex1 and Cex 2 are capacitances of the output contacts.

Ris is the resistance of the isolation, which is defined by the properties of the materials of protective coating and basis.

LR is a total equivalent inductance of the element, including the inductance of the input and output contacts.

RR is the resistance of the resistive element, the main part of the resistor.

Rcont is the equivalent resistance of the output contacts. Rcont is significant only for low-ohmic resistors

CR is the equivalent capacitance of the resistor.

Figure 4. Film resistor construction (carbon- or metal-film).

Figure 4 illustrates the resistor elements, mentioned in Figure 3.




It can be shown that for the equivalent circle of Figure 3 , the real part of the impedanceRe (Z ( f ) )

has a form:

Re (Z ( f ) )=(RR+Rcont )R is

RR+Rcont+Ris (1)

Figure 5. Example of Z ( f ) characteristics of resistor (R = 1.8 kΩ).

Figure 5 presents an example of Z ( f ) characteristics of a resistor (R = 1.8 kΩ). There is a slight

increase of |Z ( f )| and the phase (as opposite to the const values expected). Nevertheless,

accounting for the wide range of measured frequencies (100 Hz – 1 MHz), the device should be

considered as very close to the ideal one.




Equivalent circle and frequency dependence of capacitor.

Figure 6. Equivalent circle of capacitor (after [6]).

Figure 6 shows equivalent circle of capacitor. Notation:

C ex - is a total capacitance of the output contacts.

LC - is a parasitic inductance of the element, which is defined by the geometry of the capacitor’ plates. This inductance defines restrictions for usage of the specific capacitor on high frequencies.

C - is the capacitance of the capacitor, the main part of the element.

Rloss - is the resistive loss, originating from the fact, that polarization of dielectric material (of capacitor) by AC voltage demands energy. Thus, a part of the electromagnetic energy is lost.

Ris - is the resistance of the isolation, which is defined by the properties of the materials of protective coating.

Figure 7. Construction of an aluminum surface mounting electrolytic capacitor. Right upper

insertion – details of construction of a wound aluminum electrolytic capacitor (after ).




Figure 7 illustrates the capacitor elements, sketched in Figure 6.

Figure 8 presents an example of Z ( f ) characteristics of capacitor. The |Z ( f )| first falls with the

frequency increased, but then, for f >250 KHz , it begins to grow (as opposite to the ideal

model). Besides, the phase is switched from −900 (as expected) to 800

(close to that of coil). Thus

from f >250 KHz , the behavior of the device does not match that of the ideal model.


Figure 8. Example of Z ( f ) characteristics of a capacitor.

Abs

of i

mpe

danc

e |Z

(f)| [

Ω]



Equivalent circle and frequency dependence of coil.

Figure 9. Equivalent circle of coil (after [6]).

Figure 9 shows equivalent circle of coil. Here: L - is the total inductance of the coil element (including the parasitic inductance of the output

contacts)

CL - is the capacitance of the coil, originating from the capacitance of the output contacts, capacitance of the winding, core and shield.

RC

L - is the resistive loss, reflecting the energy losses in the CL capacitance.

RL - is the resistive loss, originating from the energy losses in the coil L itself.

Figure 10. Construction of an aluminum surface mounting inductor.




Figure 11. Example ofZ ( f ) characteristics of a coil.

Figure 11 presents an example of Z ( f ) characteristics of a coil. The |Z ( f )| increases almost linearly, as expected from the ideal model. As opposite to the former, the phase first increases

with the frequency (even though does not reach the expected 900 value) and then begin to

decrease. Thus the behavior of this device does not match the expected from the ideal model.




Assignments and analysis

Acquire Z ( f ) measurements for :

1 sample of resistor 1 sample of capacitor 1 sample of coilusing the Keithley measurement system (see Appendix 1 for details about pin connections and Keithley program parameters.)

(Note that the measurements supply the ABS value of the impedance,|Z ( f )| [Ω ] and the phase

angle, θ [ deg ] , as a function of frequencyf [Hz ]).

Note: after executing the measurements and before processing the acquired data, save this

Excel template on your computer (double click on the Excel icon File Save as …). Then copy the

results of the measurements (located in the measurements folder of Keithley in the subdirectory

“tests/data”) to the Excel template, saved on your computer.




Analysis of physical parameters of R, C and L components.

1. For each of the studied components, plot in Excel graphs|Z ( f )|and θ ( f ) (two curves on a single plot). Compare your results with these expected for the ideal components (see Figure 1).

2. Computation of the resistance, Re (Z ( f ) ) , and reactance, Im (Z ( f ) ) . For each of the

components, compute the values of resistance Re (Z ( f ) )=|Z (f )|cosθ ( f ) and reactance

Im (Z ( f ) )=|Z ( f )|sinθ ( f ) . Fill in the corresponding empty columns in the Excel file

Plot Re (Z ( f ) ) and Im (Z ( f ) ) (two curves on a single plot)




Final Report content.

Final Report must include the following graphs with explanations for each of the components (R, C and L):

1. Plot |Z ( f )| and θ ( f ) (one plot for each of the components)

2. Plot Re (Z ( f ) ) and Im (Z ( f ) ) (one plot for each of the components)3. Conclusions about the perfectness of the components you studied. (Compare your results with

these expected for the ideal components (see Figure 1)).




Experimental set-up and samples to be studiedThe experimental setup includes Keithley matrix and Agilent L-C-R analyzer (Figure 13).

You will use Test fixture probe station (Figure 12) (with two-pins connection table), connected by the triax

cables No 9,10,11,12 to the Keithley switching matrix.

Table 1. Samples to be studied.

Resistors coils capacitors


Keithley 708A Switching Matrix

Monitor

Figure 13. Keithley and Agilent L-C-R measurement setup.

Figure 12. Test fixture probe station.

Agilent 4284A LCR meter

Keithley SCS

4200 I-V AND Param

eter analyz

er



AcknowledgementElectrical Engineering Department of Braude College would like to thank to Adi Atias and Moran Efrony for their help in the preparation of this laboratory work.




Appendix 1 : Kite settings for Z( f ) measurements.

(the same settings for R, L and C)

1.pin connection scheme:

2.Z( f ) Keithley settings

Connect pins

Library Name sorin_4284AModule Name ZF_SweepReturn Type INT

Parameter Name In/Out Type ValueInstIdStr Input CHAR_P CMTR1

LoPin Input INT 12HiPin Input INT 11StartF Input DOUBLE 2.000000e+001StopF Input DOUBLE 1.000000e+006StepF Input DOUBLE 1.000000e+004

SignalLevel Input DOUBLE 6.000000e-002Bias Input DOUBLE 0

Range Input DOUBLE 0Model Input INT 0

IntegrationTime Input INT 1Z Output DBL_ARRAY N/A

Zsize Input INT 1350F Output DBL_ARRAY N/A

Fsize Input INT 1350D_or_R Output DBL_ARRAY N/A

D_or_Rsize Input INT 1350


LoPin (cable 12) HiPin (cable 11)Z(f)

measurements



Appendix 2 : Resistors, coils and capacitors info

1. Resistor color codes.

Resistor values are always coded in ohms (Ω). (resistor calculator)

band A is first significant figure of component value band B is the second significant figure band C is the decimal multiplier band D if present, indicates tolerance of value in percent (no color means 20%)For example, a resistor with bands of yellow, violet, red, and gold will have first digit 4 (yellow in table below), second digit 7 (violet), followed by 2 (red) zeros: 4,700 ohms. Gold signifies that the tolerance is ±5%, so the real resistance could lie anywhere between 4,465 and 4,935 ohms.

Resistors manufactured for military use may also include a fifth band which indicates component failure rate (reliability). Tight tolerance resistors may have three bands for significant figures rather than two, and/or an additional band indicating temperature coefficient, in units of ppm/K.

All coded components will have at least two value bands and a multiplier; other bands are optional (italicised below).The standard color code per EN 60062:2005 is as follows:

Color Significantfigures Multiplier Tolerance Temp. Coefficient (ppm/K)

Black 0 ×100 – 250 U

Brown 1 ×101 ±1% F 100 S

Red 2 ×102 ±2% G 50 R

Orange 3 ×103 – 15 P

Yellow 4 ×104 – 25 Q

Green 5 ×105 ±0.5% D 20 Z

Blue 6 ×106 ±0.25% C 10 Z

Violet 7 ×107 ±0.1% B 5 M

Gray 8 ×108 ±0.05% A 1 K

White 9 ×109 – –

Gold – ×10-1 ±5% J –

Silver – ×10-2 ±10% K –

None – – ±20% M –

1. Any temperature coefficent not assigned its own letter shall be markd "Z", and the coefficient found in other documentation.

2. For more information, see EN 60062.


http://www.csgnetwork.com/resistorvalimagecalc.html

http://en.wikipedia.org/wiki/File:Resistor_bands.svg

http://en.wikipedia.org/wiki/File:4-Band_Resistor.svg



2. Capacitor marking.

Capacitance values are always coded in pico-farads (pF).

Most capacitors have numbers printed on their bodies to indicate their electrical characteristics.

Larger capacitors like electrolytic usually display the actual capacitance together with the unit (for example, 220 μF).

Smaller capacitors like ceramics, however, use a shorthand consisting of three numbers and a letter, where the numbers show the capacitance in pF (calculated as XY x 10Z for the numbers XYZ) and the letter indicates the tolerance (J, K or M for ±5%, ±10% and ±20% respectively).

Additionally, the capacitor may show its working voltage, temperature and other relevant characteristics.

Example: A capacitor with the text 473K 330V on its body has a capacitance of 47 x 103 pF = 47 nF (±10%) with a working voltage of 330 V.

3. Coil color codes.

Capacitance values are always coded in micro-henries (µH). (coil calculator)


http://www.electronics2000.co.uk/calc/inductor-code-calculator.php



Bibliography and internet links1 Resistor – wikipedia: http:// en.wikipedia.org/wiki/Resistor

2 Inductor (coil) – wikipedia: http:// en.wikipedia.org/wiki/Inductor

3 Capacitor – wikipedia: http:// en.wikipedia.org/wiki/Capacitor

4 “Electronic materials” (online postgraduate course – University of Bolton).

Coils Electrolytic Capacitors Ceramic resistors and capacitors

5 Circuit book (resistors).

6 К. С. Петров. «ПАССИВНЫЕ КОМПОНЕНТЫ РАДИОЭЛЕКТРОННОЙ АППАРАТУРЫ» (Учебное

пособие). Резисторы Конденсаторы Катушки индуктивности


http://dvo.sut.ru/libr/eqp/031/23.htm



http://circuitbook.com/basic_electronics/resistors.php

http://www.ami.ac.uk/courses/topics/0135_cc/index.html

http://www.ami.ac.uk/courses/topics/0136_ec/index.html

http://www.ami.ac.uk/courses/topics/0238_ind/index.html

http://www.ami.ac.uk/courses/topics/

http://en.wikipedia.org/wiki/Capacitor

http://en.wikipedia.org/wiki/Capacitor

http://en.wikipedia.org/wiki/Inductor

http://en.wikipedia.org/wiki/Inductor

http://en.wikipedia.org/wiki/Resistor

http://en.wikipedia.org/wiki/Resistor



Preparation Questions

1. Draw the impedance graph Z (single plot) for the 3 passive components: R, C, L. (Draw the

graph in the axes Im(Z) vs Re(Z). )

2. Draw the equivalent circle of R (explain the meaning of all the elements of the circle).

3. Draw the equivalent circle of C (explain the meaning of all the elements of the circle).

4. Draw the equivalent circle of L (explain the meaning of all the elements of the circle).


snvhome.netsnvhome.net/ee-braude/devices-lab/labs/r-c-l... · web viewbraude college of...

Documents