Appendix A:

Noise Sources and Cures

Noise, random and uncorrelated fluctuations of electronic signals, finds its way into experiments in a variety of ways. Good laboratory practice can reduce noise sources to a manageable level, and the lock-in technique can be used to recover signals which may still be buried in noise.

Intrinsic Noise Sources

Johnson Noise. Arising from fluctuations of electron density in a resistor at finite temperature, these fluctuations give rise to a mean square noise voltage,

_

V2 = ∫4kT Re[Z(f)] df = 4kTR ∆ f

where k=Boltzman's constant, 1.38x10-23J/°K; T is the absolute temperature in Kelvin; the real part of the impedance, Re[z(f)] is the resistance R; and we are looking at the noise source with a detector, or ac voltmeter, with a bandwidth of ∆ f in Hz. For a 1MΩ resistor,

_

(V2)1/2 = 0.13 µ V/√ Hz

To obtain the rms noise voltage that you would see across this 1M½ resistor, we multiply

0.13µ V/√ Hz by the square root of the detector bandwidth. If, for example, we were looking at all frequencies between dc and 1 MHz, we would expect to see an rms Johnson noise of

_

(V2)1/2 = 0.13 µ V/√ Hz*(106 Hz)1/2 = 130 µ V

'1/f Noise'. Arising from resistance fluctuations in a current carrying resistor, the mean squared noise voltage due to '1/f' noise is given by

_

V2 = A R2 I2 ∆ f/f

where A is a dimensionless constant, 10-11for carbon, R is the resistance, I the current, ∆ f the bandwidth of our detector, and f is the frequency to which the detector is tuned. For a carbon resistor carrying 10 mA with R = 1k, ∆ f = f = 1Hz, we have

Vnoise = 3 µ Vrms

And Others. Other noise sources include flicker noise found in vacuum tubes, and generation and recombination noise found in semiconductors.

All of these noise sources are incoherent. Thus, the total noise is the square root of the sum of the squares of all the incoherent noise sources.

Non-Essential Noise Sources

In addition to the "intrinsic" noise sources listed above there are a variety of "non-essential" noise sources, i.e. those noise sources which can be minimized with good laboratory practice. It is worthwhile to look at what might be a typical noise spectrum encountered in the laboratory environment:

Noise Spectrum

Some of the non-essential noise sources appear in this spectrum as spikes on the intrinsic background. There are several ways which these noise sources work their way into an experiment.

40

Page 43 Page 45
Page 44
Image 44
SRS Labs Lock-In Amplifier, SR530 manual Appendix a Noise Sources and Cures, Non-Essential Noise Sources
Page 43 Page 45

SR530, Lock-In Amplifier specifications

The SRS Labs Lock-In Amplifier, model SR530, is a powerful tool designed for high-precision measurements in the realm of scientific research and industrial applications. This state-of-the-art instrument excels in extracting small signals from noisy environments, making it an invaluable asset for experiments in fields such as physics, engineering, and materials science.

One of the main features of the SR530 is its ability to perform synchronous detection, which is key to improving signal-to-noise ratios. By utilizing a reference signal, the device correlates the incoming signal with the reference to effectively filter out noise, allowing for the accurate measurement of weak signals that might otherwise be obscured. This process of phase-sensitive detection is fundamental to the operation of the Lock-In Amplifier.

The SR530 offers a wide frequency range, covering from 0.1 Hz to 100 kHz. This broad frequency response allows it to handle a diverse array of signals, making it suitable for various applications including optical detection, capacitance measurements, and in many cases, voltammetry. The device is also equipped with multiple inputs and outputs, facilitating the integration with other laboratory equipment and enabling complex experimental setups.

Precision is further enhanced with its adjustable time constant, which allows users to optimize the response time based on experimental needs. The user can choose time constants from 10 microseconds to 10 seconds, accommodating fast dynamic measurements as well as those requiring stability over longer durations.

Another remarkable characteristic of the SR530 is its digital processing capabilities. The device features a highly accurate digital voltage measurement system, minimizing drift and ensuring long-term stability. Additionally, the use of microprocessors enhances data handling and allows for features such as programmable settings, facilitating automated measurements.

Moreover, the SR530 includes a range of output options, including analog outputs, which can be used for direct signal processing, as well as digital interfaces for integration with computers. This ensures that users can not only capture high-fidelity data but also analyze and display it efficiently.

In conclusion, the SRS Labs SR530 Lock-In Amplifier stands out due to its sophisticated technology, versatile features, and robust performance. Its precision, flexibility, and ease of use make it an ideal choice for researchers and engineers looking to unlock the potential of weak signal measurement in complex environments.
Top Page Image Contents