For any electrical signal one will wish to reduce the noise as much as possible. For sensor signals this is especially true because they acquire raw data that do not lend themselves to correction schemes like communication signals do. Reducing noise is important for heat flux measurement like any sensor, and for most heat flux sensors noise is the limiting factor for low level measurements. Here we will look at theoretical noise limits, explore some common noise reduction techniques, and determine the minimum resolvable heat flux based on the theoretical noise limits.
Minimum Theoretical Noise
For most heat flux sensors, thermal noise (also called Johnson noise) provides the noise floor for a heat flux signal. The voltage created by this noise is given by:
Vn = (4kTBR)½ (1)
where k is Boltzman's constant (1.38e-23 J/K), T is the temperature in Kelvin, B is the bandwidth of the receiver in Hertz, and R is the resistance in the circuit in ohms. Other noise sources can be ostensibly eliminated, but this represents a fundamental physical limit. Even so, the noise floor can be managed to some extent, within the parameters of a given application. The most basic noise reduction can be taken directly from equation (1). Boltzman's constant obviously can't be changed, and the resistance of the sensor is fixed during production. But both temperature and bandwidth can be exploited to minimize noise.
The noise depends on the square root of the absolute temperature, so making sure the sensor has a good heat sink is not just necessary for a reliable measurement (no heat sink = no heat flow = no signal) but also reduces the potential noise. The minimum noise level is 50% higher at 400°C than it is at room temperature.
The noise also depends on the square root of the bandwidth of the receiver. The smaller the bandwidth, the less noise will be picked up. Because the bandwidth range is much greater than the temperature range, the bandwidth will typically have a much larger impact on the total noise than the temperature. In most cases a high bandwidth is only needed for fast time response, so when possible, set the bandwidth of the receiver by the Nyquist criteria:
B = 2/t (2)
where B is the needed bandwidth in Hertz and t is the needed minimum resolvable time increment in seconds. The noise level is 10 times higher for a signal that needs a time resolution of 1 ms compared to one that only needs a resolution of 100 ms.
Noise Reduction
Knowing the minimum noise level is good, but only if other noise sources can be eliminated. To reduce noise, one can either eliminate noise sources or configure the signal wires to resist noise. We will briefly examine both.
Common sources of noise are computer monitors, cooling fan motors and other motors, fluorescent lighting, high-current transformers, and line noise from the outlet. If any device appears to be making noise, the best solution is to turn it off. A constant voltage transformer can screen out the noise from the outlet, although the best solution is to run on independent batteries. Frequently the source of the noise cannot be eliminated, so the signal itself must be made as robust as possible.
When possible, sensor signals should be taken differentially instead of single-ended. In this way, noise picked up by the positive and negative legs of the signal wire will be subtracted out, leaving only the desired signal. The differential configuration works best with twisted pair wire, because the when the twisted pair picks up noise, it does so more evenly than side-by-side wire. Shielded cable is good way to screen out noise as well, although it will only affect noise that would have been picked up by the wire along its length.
Another important noise reduction technique is the elimination of ground loops. This is more easily said than done, but can result in significant noise reduction. A ground loop occurs because of slight resistances between a circuit element and the ground. That resistance can create a voltage if current leaks through it. When connecting different components in a system to a common ground, always connect them in parallel, never in series. Connections to the common ground should be through large gage, low resistance wire. Only one connection to ground should be used for each element. This can be trickier than it sounds, because there may be inadvertent connections that were not made purposely (through the mounting fixture of the sensor for instance), so testing with a good resolution multimeter can be helpful.
If there is still too much noise in the system, there are also some data acquisition techniques that can help. The most basic is to average data over some interval, which will tend to make high and low noise peaks cancel each other out. This essentially limits the bandwidth, and hence the time response, by requiring many samples to be taken for each data point. The advantage here is that it can be done post-processing, so that the time-response versus noise level can be easily optimized. For slower signals, the data can be passed through a low-pass filter to screen out high frequency noise. Fast signals need the high order frequencies to be accurately represented, so filtering techniques are less applicable.
Minimum Resolvable Heat Flux
The minimum resolvable heat flux will depend on two things, the type of sensor being used and the desired signal-to-noise ratio (SNR). The required SNR will depend somewhat on the application, although typically a SNR of 1000 is considered good. A SNR of 100 is reasonable, but the accuracy will not be as high. Some useful information can even be obtained from a SNR of 10, although only order of magnitude measurements. Any SNR below 10 is probably junk data. The type of sensor will also of course depend on the application, but for noise purposes the only important parameter is the resistance of the sensor. Here are some examples of minimum resolvable heat flux for Vatell sensors. We see again that the fastest sensors have to deal with the most noise.
For an HFM with a resistance of 3.6 kohms operating at 127°C (400 K) and being interrogated at 100 kHz to take full advantage of its time response, the minimum noise is 2.8 mV. Assuming the HFM has a sensitivity of 150 mV/W/cm² and we want a SNR of 100, the minimum resolvable heat flux is 1.9 W/cm². If we drop the needed time response to 1 kHz, our minimum resolvable heat flux is 0.19 W/cm².
For a Thermogage sensor with a resistance of 1 ohm operating at 127°C and being interrogated at 100 Hz for the fastest sensor, the minimum noise is 1.5 nV. Assuming the Thermogage has a scale factor of 2000 W/cm²/mV (which is a sensitivity of 0.5 mV/W/cm²), and we want a SNR of 100, the minimum resolvable heat flux is 0.3 mW/cm², or 3.0 W/m².
For a BF sensor with a resistance of 49 ohms operating at 127°C and being interrogated at the fastest reasonable rate of 10 Hz, the minimum noise is 3.3 nV. Assuming the BF has a sensitivity of 50 mV/W/cm², and we want a SNR of 100, the minimum resolvable heat flux is 6.6 mW/cm², or 0.066 W/m².
Fuente: www.vatell.com/Noise%20Reduction.doc
Nombre: Carlos L. Briceño R
Materia: CRF 
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