Voltage to Current converter with Floating Load

Dr Inderbir Kaur Operational Amplifiers and Applications Covid 19Week -4(05-12April2020) Reference study material

Voltage to Current converter with Floating Load

Circuit: voltage to current converter in which load resistor RL is floating (not connected to ground).

As we can see in the circuit above the input voltage is applied to

the non-inverting input terminal and the feedback voltage across R

drives the inverting input terminal.

This circuit is also called a current series negative feedback,

amplifier because the feedback voltage across R depends on the

output current iL and is in series with the input difference voltage

Vd.

Writing the Kirchoff’s voltage equation for the input loop.

Vin = Vd + Vf

But vd ≈ 0, since A is very large, therefore,

Ib


Vin = Vf

Vin = R iin

iin = Vin / R.

since Ib = 0

Hence iL = Vin / R.

Or we can say that input voltage Vin is converted into an output current

of Vin / R.

The value of load resistance does not appear in this equation.

Therefore, the output current is independent of the value of

load resistance. Thus the input voltage is converted into

current.

Applications

The voltage to current converter can be used in low voltage dc and ac

voltmeters, diode match finders, light emitting diodes and zener diode

testers.


Logarithmic Amplifier

A logarithmic amplifier, or a log amplifier, is an electronic

circuit that produces an output that is proportional to the

logarithm of the applied input.

CIRCUIT 1

In the above circuit, the non-inverting input terminal of the

op-amp is connected to ground. That means zero volts is

applied at the non-inverting input terminal of the op-amp.

According to the virtual short concept, the voltage at the

inverting input terminal of an op-amp will be equal to the

voltage at its non-inverting input terminal.

+ VE

-


So, the voltage at the inverting input terminal will be zero

volts. We can say that the collector is at virtual ground and

since base is also grounded, the transistor’s voltage current

relationship becomes that of a diode and is given by

IE = IS (e[ q VE

/ KT] -1) (1)

IS = the saturation current,

k = Boltzmann’s constant

T = absolute temperature (in K)

Since IE = IC for grounded base transistor,

IC = IS (e[ q VE

/ KT] -1) (2)

(IC/IS) = (e[ q VE

/ KT] -1) (3)

or

e[ q VE

/ KT] = (IC/IS) + 1 (4)

Since IC >> IS , (as IS ≈ 10-13 A )

e[ q VE

/ KT] ≈ (IC/IS) (5)

Taking natural log on both sides of the above equation, we get

VE = kT/q ln ( IC / IS ) (6)


In figure above (circuit 1)

The collector current IC = Vin/Ri and Vout = -VE

Therefore,

Vout = -(kT/q) ln[Vin/Ri.IS] (7)

VOUT = -KT/q ln(Vin /Vref) (8)

Where Vref = RiIS

The output of the circuit is, thus, proportional to the log of the input voltage.

Limitations of circuit1

The output voltage is directly proportional to the circuit temperature, T.

Is can vary considerably from transistor to transistor, and is also temperature sensitive, approximately doubling for each 10 C° rise.

Compensation circuits can be added to stabilize the output against these variations.

Figure (circuit 2) below shows log amplifier with saturation current and

temperature compensation


CIRCUIT 2

The input Vi is applied to one log amplifier and a reference voltage

is applied to annother log amplifier.

The two transistors are integrated close together in a same silicon

wafer. This provides a close match of saturation currents and

ensures good thermal tracking.

Assume

IS1 = IS2 = IS

Then V1 = -(kT/q) ln[V i/ R1.IS] (9)

And V2 = -(kT/q) ln[Vref / R1.IS] (10)

Now from the circuit above we can see that


VO = V2 - V1

Or VO = (kT/q) [ ln(Vi / R1.IS) – ln(Vref / R1.IS) ] (11)

Or VO = (kT/q) [ ln(Vi / Vref ] (12)

Thus reference level is now set with a single external

voltage source. Its dependence on device and temperature

has been removed.

The voltage VO is still dependent on temperature and is

directly proportional to T. this is compensated by the last

opamp stage A4 .

A4 provides a non inverting gain of ( 1+ R2 / RTC ).

Hence the output voltage is

VO.COMP = ( 1+ R2 / RTC ) (kT/q) [ ln(Vi / Vref ]

Where RTC is a temperature sensitive resistant with a positive

temperature coefficient of temperature so that the slope of the

equation becomes constant as the temperature changes.

Limitation of circuit 2

The circuit requires four opamps and becomes expensive.


Antilog Amplifier

A circuit to convert logarithmically encoded signal to real signals.

CIRCUIT 3

The input Vi for the antilog-amp is fed into the temperature

compensating voltage divider R2 and RTC and then to the base of

Q2.

The output of VO of the antilog amplifier is fed back to R1 at the

inverting input of op amp A1.


The non-inverting inputs are grounded

The base to emitter voltage of transistors Q1 and Q2 can be written as

VQ1 B-E = (kT/q) [ ln(VO / R1 IS ] (1)

VQ2 B-E = (kT/q) [ ln(Vref / R1 IS ] (2)

Since Base of Q1 is tied to ground, we get

VA = - VQ1 B-E = - (kT/q) [ ln(VO / R1 IS ] (3)

The base voltage VB of Q2 is

VB = ( RTC / R2 + RTC ) Vi (4)

The voltage at the emitter of Q2 is

VQ 2E = VB + VQ 2 E-B (5)

Hence using eqn. 2 and 4, we get

VQ 2E = ( RTC / R2 + RTC ) Vi - (kT/q) [ ln(Vref / R1 IS ] (6)

We can see from the circuit that emitter voltage of Q2 = VA ,

VA = VQ2 E

Using eqn.3 and 6

- (kT/q) [ ln(VO / R1 IS ]= ( RTC / R2 + RTC ) Vi - (kT/q) [ ln(Vref / R1 IS ] (7)

Or ( RTC / R2 + RTC ) Vi = - (kT/q){ [ ln(VO / R1 IS ]- [ ln(Vref / R1 IS ] } (8)


Or - (q/kT)( RTC / R2 + RTC ) Vi = ln(VO / Vref ) (9)

We know that Log10 x = 0.4343 ln (x)

- 0.4343 (q/kT)( RTC / R2 + RTC ) Vi =0.4343 ln(VO / Vref ) (10)

-K’ Vi = log10 (VO / Vref ) (11)

Or (VO / Vref ) = 10- K’ Vi (12)

VO = Vref (10- K’ V

i )

Where K’ = 0.4343 (q/kT)( RTC / R2 + RTC )

Hence an increase of input by one volt causes the output to

decrease by a decade.

For further understanding you can also refer to NPTEL

video (Lecture 36)

https://nptel.ac.in/courses/122/106/122106025/

DISCLAIMER: This study material is only for the reference of students. No copyright infringement is

intended. This is only for the emergent situation of Covid period only where students don’t have

access to other reading material.

References : 1 Opamps and linear integrated circuits technology : Ramakatnt A. Gayakwad



2 linear integrated circuits by D. Roy Chaudhary and Shail Jain 3 https://nptel.ac.in/courses/117/107/117107094/ 4 www. Circuitstoday.com

5 https://www.electronics-tutorials.com


https://www.electronics-tutorials.com/

Voltage to Current converter with Floating Load

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