Nuts & Volts - February 2006

I

N

T

H

E

T

R

E

N

C

H

E

S

Mode Rejection Ratio) needed and how accurate must the voltage reference be?

Using Ohm's law, it's found that the load resistance at 10 amps and 35 volts is 3. 5 ohms. Let's choose a 0.01 ohm sense resistor placed in the high-side (+ 35 volt lead) and measure the voltage developed across it to determine the current flowing through it (the standard method). Ten amps through 0.01 ohms will create a 0.1 volt signal (and generate one watt of heat so we'll use a five-watt resistor). Using the order-of-magnitude rule, we must measure with 1 mA resolution. This means that if 0.1 volt equals 10 amps, then 10 microvolts equals 1 mA (a factor of 10,000). This 10 microvolts is measured in the presence of 35 volts of common-mode voltage which is a ratio of 3,500,000 or a CMRR of about 131 dB. (This really isn't that hard to do.)

The reference accuracy must be one part in 10,000 or 0.01%. This is defined by the ratio of the smallest measurement ( 10 microvolts) and the largest measurement (0.1 volts). Note that this includes the order-of-magnitude rule. If you want to digitize this, you will need about 13 bits of resolution (one part in 8,192). Since 13-bit A/Ds are not common, you will have to choose between a 12-bit (one part per 4,096) or 14-bit (one part per 16,384) A/D. The choice will depend on many factors, including cost.

NON-STANDARD INSTRUMENTATION

As time passes, standard techniques are developed for typical instrumentation applications. The analog VOM (Volt-Ohm-Milliammeter) is still a very useful instrument and was once the standard instrument for all engineers, technicians, and hobbyists. Way back then, no one could conceive of anything else. But time passes. With the advent of digital and uP technology, modern multimeters provide capabilities that were once impossible to imagine or realize. It's now common for these inexpensive

digital meters to measure capacitance, inductance, frequency, and even test semiconductors. Many times, the traditional methods work well. There is certainly a lot of history and experience associated with them. But it's always useful to look at new ways, too. It is not uncommon for standard instrumentation practice to lag behind technical advances. And naturally, creativity can always be applied. Let's look at a couple of examples.

A common requirement is the generation of a low-distortion sine wave. There are lots of ways to do this. There are analog methods like the Wien-bridge oscillator (made famous by H/P), L-C oscillators, crystal oscillators, phase-locked-loops, etc. The digital method typically uses a D/A (Digital-to-Analog converter) to create the sine wave in steps. There are a number of variations of this method which include the NCO (Numerically-Controlled-Oscillator). Don Lancaster has spent considerable time generating special digital patterns that can be easily filtered to create “magic sine waves.”

However, there is another method that seems neglected: switched-capacitor filters. These devices use a combination of analog and digital techniques to create “universal” filters of nearly any type (Butterworth, Bessel, Elliptic, etc.) and of high-order (very sharp response). It's very easy to create (or buy) a sharp-cutoff low-pass filter with a stop-band only 100% higher than the pass-band. This means that if you put a square wave into the filter with a frequency near the high edge of the pass-band frequency, the higher harmonics are filtered out, leaving a nice, digitized sine wave. There are typically 50 or 100 steps in the sine wave (due to the digital clock of the filter). These are easily filtered out with a simple R-C filter. But wait! There's more!

The cutoff frequency of the filter is locked to the clock frequency. This means that if you use a derivative of the clock as the input square wave, the output sine wave will track perfectly with the clock. You have a very

simple and inexpensive sweepable, sine wave generator that can be digitally controlled. Since it's a filter, rather than an oscillator, the output amplitude is very stable. Since it's based on a digital clock, the frequency is extremely stable. In short, the switched-capacitor-filter is a very useful sine wave generator.

MEASUREMENT CONVERSIONS

It is often very useful to convert a difficult-to-measure property into something that is easier to measure. As we saw in the above current-measuring exercise, we converted a current into a voltage by using a “sense” resistor. It's hard to measure current directly. Even analog meters convert current into a magnetic field to deflect a pointer. Measuring current directly means counting electrons. I'm sure that's possible, but I'm also sure that it's not practical for most applications. Whenever you are tasked to measure something difficult, it's often useful to stop and think of as many different conversions as you can.

Let's look at a real example. A while back, I worked for a company that made gravimeters (a device that measures local gravity with high precision). They wanted a “New Method.” The old method was actually very sensitive and used a coil of wire held between magnets with an electric current. The position of the coil was measured capacitively. There were two problems. The magnets changed their magnetism over time and the “spring” that supported the coil also changed over time. With gravimeter sensitivity in the parts-per-million range, it took very little change in these parts to create a significant measurement change. In fact, the rate of change for these parts was measured and applied to all measurements. A workable, if not elegant, approach.