If you stay active as a design engineer long enough, I'm convinced that sooner or later you will be faced with the problem of digging analog signals out of the mud.
Sometimes this daunting task is encountered within our own designs. Sometimes we are just trying to measure a signal, or the output of a sensor. Regardless, this measurement problem can be particularly difficult at very low frequencies due to thermal-electric effects and 1/f noise, noise with an amplitude that continues to increase as the frequency is reduced. Measurements outside the 1/f noise region are almost routine. Choose the lowest noise device that you can get to begin with, and find a way to average (or to continually narrow the measurement bandwidth), and that's that.
Let's consider the bandwidth for a moment. We have two frequency cutoffs to consider, one at the upper and one at the lower band edge. By inspection, the lower band edge is constrained by the total signal observation time. For example, if I measure a signal for 1 second, it should be obvious that I could not possibly observe a 0.001Hz noise. A 0.001Hz noise will not change much in 1 second. However, if I were to open my measurement window to 1,000 seconds, I would see a single cycle of the low frequency noise term, without any attenuation. It turns out that the total signal observation time determines the low frequency cutoff frequency. The high frequency cutoff is determined from the bandwidth of the ADC used to make the measurement. Longer apertures (a fancy name for the integration window) lower the high frequency cutoff while short apertures raise the high frequency cutoff.
The usual plan of attack to lower noise is to play the “narrow the bandwidth” game. Now that we can find the upper and lower cutoff frequency, we need to find the narrowest band that still contains the desired signal, or we need to find a way to put the desired measurement within our narrow bandwidth. Phrasing the question this way allows us to discover the value of the chopper, lock-in amplifier, or of the dc reversal technique. All these techniques are really playing the same game — a game we play in radio as well. Here we are just moving the signal into our narrow band outside of the 1/f noise region. I will save the details of explaining how each of these techniques work for another blog.
Now that we have talked a little about measuring odd voltages, let's discuss circuits and devices that require a stimulus. First, let's consider the impedance of the load at the measurement frequency. Below in Figure 1, two load impedances are plotted.
In each case, source noise on the voltage stimulus (left figure) and current noise on the current source (right figure), will not generate significant measure noise.
From the figure it should be obvious why low impedance devices are measured by using a current stimulus and high impedance devices are interrogated with a voltage stimulus. For a low impedance device, small changes (noise) in the stimulus current will not generate much of a deviation in the voltage measurement. Likewise, for a high impedance device, noise in the voltage stimulus will not result in current noise. Careful consideration of the chart will reveal that using the opposite method will yield noisy results. Always, always consider the value of the impedance. The equations for Johnson noise voltage and Johnson noise current are shown below:
Find the p-p noise associates with the impedances that you are using in your circuits or sensors. Johnson noise is REAL.
Finally, let's consider the parts themselves. Today let's just discuss thermals, since we have been talking about low-frequency noise (saving time drift and temperature coefficient for another blog). It turns out not to be so easy to predict thermal drift; however, there is a great test that can be used to predict just how good a part (including the layout) will perform at very low frequencies. Here is how it works: Bias up, or connect up your part or circuit in an oven set for 25°C. Next, step the temperature to 50°C and watch the output voltage. After the circuit reaches thermal equilibrium again at 50°C step the temperature back to 25°C. Do all this while measuring the output voltage of the sensor or circuit. See Figure 2 below:
When you consider your circuit, sensor, or layout for its low thermal performance, there are really two issues. The first involves the actual materials used. Thermal voltages (unintentional thermocouples) are created whenever dissimilar materials are brought together (including the silicon and bonding wires inside your op-amps). The thermal voltages are generated along the length of the materials themselves. Thermal voltages cannot be avoided completely.
The second issue to consider is the thermal time constant. Look for a moment at the figure above. Here, the height of the thermal voltage is a function of the materials used, but the recovery time describes this circuit or components thermal time constant. Essentially a measurement of how fast the parts construction materials reach thermal equilibrium. We want this to be as fast as possible. If this time constant is much faster than the circuit or parts environmental thermal transient, your thermal voltages will be small. This test really generates comparative results between different parts, or layouts rather than hard numbers. For a more in-depth discussion, please see the following:
Like Bugs Bunny would say, “Thats all folks!” Another time we'll talk about coupled noise sources and shielding/grounding problems.