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17
Differential Connection (A-B)
The second method of connection is the differential mode. This mode has two signals cables which connect the signal
source and the lock-in's inputs. There are two high impedance power amplifiers in the lock-in. The lock-in measures the
voltage difference between the center conductors of the A and B inputs, which can avoid common voltage problems since
the shields are ignored.
In this mode, take care that the two cables travel the same path between the experiment and the lock-in. There should not
be a large loop area enclosed by the two cables. Otherwise, measurement is susceptible to magnetic pickup.
1.10
Intrinsic Noise Sources
Noise is defined as any negative factors which will affect the result of measurement. Noise is random, unpredictable and
temporary. Good experimental design should reduce the noise and improve the stability and accuracy of measurement.
There are various intrinsic noise sources which are present in all electronic signals. Some of them are unavoidable which
only can be decreased by signal averaging and a narrower bandwidth. Others can be decreased by filtering and perfect line
structures and component layout. Meanwhile, amplifier itself also produces noise at work, which can be solved by low
noise amplifier design techniques.
Johnson Noise
Every resistor generates a noise voltage across its terminals due to thermal fluctuations in the electron density within the
resistor itself. This is Johnson noise. The spectrum of the Johnson noise is flat, so the noise power is almost the same in
different frequency band (of course there is an upper limit frequency). In this case, the noise is called white noise. The
fluctuations give rise to an open-circuit noise voltage,
2
1
)
4
(
kTRB
V
Where k=1.38
×
10
-23
J/
°
K is the Boltzmann's constant. T is the temperature in
°
Kelvin, which can be transformed to
°
Celsius:
°
K=
°
C +273.16. R is the resistance in Ohms, and B is the bandwidth of the measurement in Hz.
Harry Nyquist's mathematical studies of Johnson noise revealed that the power spectrum function of Johnson noise is:
)
/
(
4
)
(
2
Hz
V
kTR
f
St
At 300
°
K, a resistor of 10 k
Ω
is connected to the input of the amplifier. The voltmeter is connected to the output of the
amplifier. The open-circuit effective voltage of the filter which has a 10 kHz bandwidth is 1.3
μ
V.
The amplitude of Johnson noise is unpredictable in normal cases. It follows the Gaussian distribution. Johnson noise is the
minimum value of the noise voltage of any devices including detectors, signal sources and amplifiers with resistors.
Johnson noise is a typical case of wave dissipation.
Shot Noise
