TS615
Noise Measurements
On a 1Hz bandwidth the thermal noise is reduced to
4kTR
where k is Boltzmann's constant, equals to 1374 x 10-23J/°K. T is the temperature (°K).
The output noise eNo is calculated using the Superposition Theorem. However eNo is not the 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.
eNo = V12 + V22 + V32 + V42 + V 52 + V62
Equation 1
eNo2 = eN2 × g2 + iNn2 × R22 + iNp2 × R 32 × g2
… + RR-----21-- 2 × 4kTR1 + 4kTR2 + 1 + RR-----21-- 2 × 4kTR3
Equation 2
The input noise of the instrumentation must be extracted from the measured noise value. The real output
noise value of the driver is:
eNo = (Measured)2 – (instrumentation)2
Equation 3
The input noise is called the Equivalent Input Noise as 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 the fifth term of Equation 2 we obtain:
eNo2
=
eN2
×
g2
+
iNn2
×
R22
+
iNp2
×
R32
×
g2…
+
g
×
4kTR2
+
1
+
RR-----21--
2
×
4kTR3
Equation 4
7.1 Measurement of eN
If we assume a short-circuit on the non-inverting input (R3=0), Equation 4 becomes:
eNo = eN2 × g2 + iNn2 × R 22 + g × 4kTR2
Equation 5
In order to easily extract the value of eN, the resistance R2 will be chosen as low as possible. On the
other hand, the gain must be large enough:
l R1=10Ω, R2=910Ω, R3=0, Gain=92
l Equivalent Input Noise: 2.57nV/√Hz
l Input Voltage Noise: eN=2.5nV/√Hz
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