4kT R∆F

Where ΔF is the specified bandwidth, and k is the Boltzmann's constant, equal to 1,374.10-23J/°K. T is the

temperature (°K).

On a 1 Hz bandwidth the thermal noise is reduced to:

4kT R

The output noise eNo is calculated using the superposition theorem. However, eNo is not the simple sum of all

noise sources but rather the square root of the sum of the square of each noise source, as shown in Equation 1.

Equation 1

eN o

V1

2

V2

2

V3

2

V4

2

V5

2

V6

2

+

+

+

+

+

=

Equation 2

eN o

2

eN

2

g

2

iN n

2

R2

2

iNp

2

+

×

+

×

R3

2

×

g

2

×

R2

R1

--------

2

4kTR 1 4kTR 2 1

R2

R1

--------

+

2

4kTR 3

×

+

+

×

+

=

The input noise of the instrumentation must be extracted from the measured noise value. The real output noise

value of the driver is shown in Equation 3.

Equation 3

eNo

Mea sure d

(

)

2

ins trumen tatio n

(

)

2

–

=

The input noise is called equivalent input noise because it is not directly measured but is evaluated from the

measurement of the output divided by the closed loop gain (eNo/g).

After simplification of the fourth and fifth terms of Equation 2, you obtain Equation 4.

Equation 4

eNo

2

eN

2

g

2

iN n

2

R2

2

iN p

2

+

×

+

×

R3

2

×

g

2

×

g

4kTR2 1

R2

R1

--------

+

2

4kTR 3

×

+

×

+

=

6.2.1

Measurement of the input voltage noise eN

Assuming a short-circuit on the non-inverting input (R3 = 0), from Equation 4 you can derive Equation 5.

Equation 5

eN o

eN

2

g

2

iN n

2

R2

2

g

4kTR2

×

+

×

+

×

=

To easily extract the value of eN, the resistance R2 must be as low as possible. On the other hand, the gain must

be high enough. R3 = 0 and gain (g) = 100.

6.2.2

Measurement of the negative input current noise iNn

To measure the negative input current noise iNn, R3 is set to zero and Equation 5 is used. This time, the gain

must be lower in order to decrease the thermal noise contribution. R3 = 0 and gain (g) = 10.

6.2.3

Measurement of the positive input current noise iNp

To extract iNp from Equation 3, a resistance R3 is connected to the non-inverting input. The value of R3 must be

selected so that its thermal noise contribution is as low as possible against the iNp contribution. R3 = 100 Ω and

gain (g) = 10.

6.3

Intermodulation distortion product

The non-ideal output of the amplifier can be described by the following series of equations.

2

in

C

n

in

+

+

+ ...

=

RHF310A

Intermodulation distortion product

DS6201 - Rev 7

page 13/25