Nonlinear resistive networks (setting of the operation point)

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Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial* framework**

Consortium leader

PETER PAZMANY CATHOLIC UNIVERSITY

Consortium members

SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER

The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund ***

**Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben

***A projekt az Európai Unió támogatásával, az Európai Szociális Alap társfinanszírozásával valósul meg.

PETER PAZMANY CATHOLIC UNIVERSITY

SEMMELWEIS UNIVERSITY

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Peter Pazmany Catholic University Faculty of Information Technology

ELECTRICAL MEASUREMENTS

Nonlinear resistive networks (setting of the operation point)

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(Elektronikai alapmérések)

(Nemlineáris rezisztív hálózatok (munkapontszámítás) )

Dr. Cserey György

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Electrical Measurements: Nonlinear resistive networks

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Nonlinear resistance

• The simplest type of non-linear networks is a nonlinear resistive network, which contains the combination of voltage sources, power supplies, linear and nonlinear invariant resistors.

• The characteristics of connection of the u voltage of the

nonlinear resistance and the i current of nonlinear resistance can be given by

i =I(u); I(0) = 0

voltage controlled explicit form, or u=U(i); U(0) = 0

current controlled explicit form, here U, and respectively I are functions.

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Typical characteristics of a nonlinear component

U I

U i

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Nonlinear components

• From the equation of the p=ui follows that the nonlinear resistance is passive if the signs of U and I have

symmetric reference directions, so the curve is located in the I. and III. parts of the plane.

• The non-linear characteristics can be given as a

characteristic curve, or as a matrix containing numbers or as a combination of elementary functions. Covering the whole range by a close approximation with a simple function is not easy to find. Fractionally linear

characteristics are often used to cover the range.

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Operation point

• Consider a resistive network, which contains only one nonlinear resistor. Replace the rest of the network by the Thevenin or Norton equivalent of the corresponding

non-linear resistor. This characteristic of this

replacement can be given by an equation of a straight line in the given t time, where this line is called load

line. The intersection points of characteristic curve of the non-linear resistance and this load line are the operation points, which can satisfy both the characteristic of nonlinear resistant and the characteristic of the rest of the network.

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Operation point

1KΩ

260V 400V

400 400

I, mA

U, V

1KΩ

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Diode characteristics - review

u i

Breakdown range

Reverse range

exponen-

tial range Linear range

Forward range

Not allowed region

Pd_max

Zenner effect

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Diode characteristics - review

• Breakdown range: The range where the Zenner effect occurs.

• Zenner effect: If the emptied layer has a sufficiently big field strength, then it is able to tear out electrons from their ties and this way free charge carriers appear.

• Reverse range: The voltage range where there is no current in the semiconductor.

• Forward range: The voltage range where there is current in the semiconductor.

• Linear range: The part of the forward range, where the voltage- current function can be approximated linearly.

• Exponential range: The part of the forward range, where the

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Diode operation point - review

Um [V]

I [mA]

U [V]

Im [mA]

maximum current Real characteristic

Operation point

Load line

maximum voltage

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Diode operation point - review

• Operation point: All the electrical characteristics set on an

electronic device. In the absence of input signal, values of the static operation point can be measured, in case of a dynamic input the current operation point is constantly changing

depending on the input signal.

• Maximum current: The value of the load line of the diode in case of zero voltage value.

• Load line: The load line represents the relationship between current and voltage in the linear part of the circuit.

• Maximum voltage: The value of the load line of the diode in case of zero current value.

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Operation point calculation

1KΩ

Ud Um=1V

• We assume that

• Ud=0.65 V

• Voltage Um-Ud that is 350 mV

• The current is

350mV/1KΩ=350μA

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Operation point calculation

500Ω

Um=1V Ud

• We assume that

• Ud=0.65 V

• Voltage 350mV that is 175 mV on both

resistances

• The current is

175mV/500Ω=350μA

^500Ω

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Operation point calculation

1KΩ Um=1V

• We assume that

• Ud=0.65 V

• Voltage 350mV

• The current is 350μA

• I

_R2

=Ud/R2=650 μA

1KΩ R2 Ud

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Operation point calculation

1KΩ

Ud Um=1V

• We assume that

• Ud=2.00 V

• Voltage Um-Ud that is -1V

• The current is = 0A!

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Operation point calculation

1KΩ

Uz Um=4V

• We assume that

• Ud=2.7 V

• Voltage Um-Ud that is 1.3V

• The current is

2.3V/1K Ω=1.3mA

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U1 I

U2

I I

G U

Kirchhoff’s voltage law

U = U1+U2

Σ ^{U = 0}

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I1

I I

G

U

Kirchhoff’s current law

I = I1+I2+I3

Σ ^{I = 0}

I2 I3

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Operation point calculation

100Ω Um=4V

• We assume that

• Uz=2.7 V

• U1=1.3V

• The current is

I=1.3V/100 Ω =13mA

• I

_R2

=2.7V/10K Ω =270μA

• I

_z

=I-I

_R2

=12.73mA

^10KΩ

R2 Uz

U1

I_z I

I_R2

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Operation point calculation

200Ω Um=4V

• We assume that

• Uz=2.7 V

• U1=1.3V

• The current is

I=1.3V/200 Ω =6.5mA

• I

_R2

=2.7V/10K Ω =270μA

• I

_z

=I-I

_R2

=6.23mA

^10KΩ

R2 Uz

U1

I_z I

I_R2

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Circuit for measurement

• I

_b

=(U

_bb

-U

_b

)/22K Ω

• I

_c

=(U

_cc

-U

_c

)/150 Ω

• To be depicted:

I

_c

(U

_ce

) in the case of I

_b

= constant

CC

P1

U_c 5V

BB BC182

P2

22KΩ

150Ω

Ground

U_b

B C

E

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Bipolar transistor

Saturation mode:

• i

_C

= ß·i

_B

• U

_BE

= 0.65 V

• U

_CE

= Vsat ≈ 0.2 V

U_C U_B

U_E

(BE: open, CB: open)

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Bipolar transistor

• The transistor can be managed as a four-pole if we duplicate one of its three terminals. The common point of the input and the

output is the ground. Thus, from an AC point of view we can distinguish three basic circuits: the common emitter, common collector, common base.

• To operate the transistor, an appropriate base-emitter voltage

signal (in case of silicon it is approx. 0.65 V) should be provided.

The direction of the collector-base voltage should be closed. The direct voltage and direct current are related to the operation point.

The changes around the operation point are for the alternating mode. During operation, direct current and alternating current quantities can be measured.

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Circuit for measurement

• We do not measure current!

• U

_gg

= U

_g

!!!

• I

_d

=(U

_DD

-U

_d

)/150 Ω

• To be depicted: in the case of I

_d

(U

_ds

)

U

_gs

= constant

DD

P1

U_d 5V

GG IRF740

P2

100Ω

150Ω

Ground

U_g U_s I_d

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MOS transistor

• Saturation mode U

_DS

≥ (U

_GS

-V

_T

) I

_D

=K/2 · (U

_GS

-V

_T

)

²

• Triode mode U

_DS

≤ (U

_GS

-V

_T

) I

_D

=K( (U

_GS

-V

_T

) · U

_DS

-U

_DS²

/2 )

where V

_T

is the threshold voltage and K is usually given

U_D U_G

U_S

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OPT2

P1

U_out 5V

P2 OPT1 2.4KΩ

Ground TCST 2000

Optocoupler

• We do not measure current!

U_in 680Ω

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Optocoupler

• Linear mode

I _c =K _opto · I _LED

U_out U_in

I_LED I_c

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Operation point calculation

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Solution process

• First step, since we are dealing with DC circuits, we can replace the capacitors with splits and coils with shortcuts.

• It is assumed that the diodes are opened mode and this can change if we get a contradiction.

• Usually the voltage of the diodes are given, in case of opened mode we can assume that this is 0.65V.

• We use the calculation rules related to the cases of serial and parallel resistors.

• We use Kirhoff's voltage and current laws.

• The basis current of the bipolar transistor usually can be negligibled.

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Solution process

• The emitter - collector voltage of the bipolar transistor can not be calculated directly.

• If we know the voltages at the poles of a resistance, the voltage difference can be calculated easily.

• We use Ohm's law. If at least two are known out of the voltage of the resistance, the resistance value and the current, then the third can be calculated on the basis of the formula U = IR.

• It is assumed that the MOS transistor is in satruation mode, if we get a contradiction in the calculation, change the assumption (triode mode).

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U_d = 0,65 V 11,35

0,65

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0,65 11,35 V

I=U/R=10,7V/R=1,7mA R=R1+R2+R3=7.1K Ω

1,507

U=I*R

9,99

5,02

0,65

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5,02

4,37

• Saturation mode: i

_C

= ß·i

_B

• U

_BE

= 0.65 V

• Saturation: U

_CE

= Vsat ≈ 0.2 V

4,37

2,19 I=U/R

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2,19 mA

11,01 U=R*I 12 V

U

_DS

≥ (U

_GS

-V

_T

), I

_D

=K/2 · (U

_GS

-V

_T

)

²

-> U

_GS

=3V

9,99 V

6,99

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6,99 9,99

11,01

4,37

10,36

We assume that

Ud=0.65 V

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11,01

10,36

2,7 3,35

5

I=U/R = (10,36 – 3,35) / 1,4 = 5 mA

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5 5

I

_c

=K

_opto

· I

_LED

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5

5 1,5

U=R*I

U

_GS

=3,5V

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U

_DS

≥ (U

_GS

-V

_T

), I

_D

=K/2 · (U

_GS

-V

_T

)

²

-> I

_D

=3,28mA

3,28

3,28 8,28

5

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8,28 6,34

6,34

3,28 5,36

U=R*I

Nonlinear resistive networks (setting of the operation point)

ELECTRICAL MEASUREMENTS

Nonlinear resistive networks (setting of the operation point)

Nonlinear resistance

Typical characteristics of a nonlinear component

Nonlinear components

Operation point

Operation point

Diode characteristics - review

Diode characteristics - review

Diode operation point - review

Diode operation point - review

Operation point calculation

• We assume that

• Ud=0.65 V

• Voltage Um-Ud that is 350 mV

• The current is

350mV/1KΩ=350μA

Operation point calculation

• We assume that

• Ud=0.65 V

• Voltage 350mV that is 175 mV on both

resistances

• The current is

175mV/500Ω=350μA

Operation point calculation

• We assume that

• Ud=0.65 V

• Voltage 350mV

• The current is 350μA

• I

=Ud/R2=650 μA

Operation point calculation

• We assume that

• Ud=2.00 V

• Voltage Um-Ud that is -1V

• The current is = 0A!

Operation point calculation

• We assume that

• Ud=2.7 V

• Voltage Um-Ud that is 1.3V

• The current is

2.3V/1K Ω=1.3mA

Kirchhoff’s voltage law

U = U1+U2

Σ U = 0

Kirchhoff’s current law

I = I1+I2+I3

Σ I = 0

Operation point calculation

• We assume that

• Uz=2.7 V

• U1=1.3V

• The current is

I=1.3V/100 Ω =13mA

• I

=2.7V/10K Ω =270μA

• I

=I-I

=12.73mA

Operation point calculation

• We assume that

• Uz=2.7 V

• U1=1.3V

• The current is

I=1.3V/200 Ω =6.5mA

• I

=2.7V/10K Ω =270μA

• I

=I-I

=6.23mA

Circuit for measurement

• I

=(U

-U

)/22K Ω

• I

=(U

-U

)/150 Ω

Σ ^{U = 0}

Σ ^{I = 0}

I _c =K _opto · I _LED