Evaluation Engineering - December 2008 - (Page 28)

NANOELECTRONICS TEST treated identically. Both have the same input characteristics, not just for intentional signals but for unintentionally coupled noise as well. Of course, real circuitry isn’t perfect although the common mode rejection ratio (CMRR) can be high to a few hundred kilohertz. LeCroy’s DA1855A Differential Ampliﬁer is a good example, being speciﬁed out to 100 MHz and with typically 115 dB CMRR at 100 kHz and 10x gain. A number of approaches have been developed to deal with low-level signals that often are buried in a much larger noise signal. The most common method is averaging. If the noise signal really is random, then its rms value will reduce as the square root of the number of averages. For example, with 100 averages, the noise will be 10x less. That sounds like an easy way to recover small signals, but averaging isn’t always appropriate. Noise levels can easily be much greater than 10x the desired signal so a great deal of averaging could be required and take a large amount of time. During that time, the desired signal also is being averaged. Ideally, it shouldn’t change from acquisition to acquisition. Another way to minimize noise is to reduce bandwidth through ﬁltering or some means other than averaging. The amount of Johnson noise is directly proportional to the square root of bandwidth, and a very small signal bandwidth is the key to the operation of lock-in amplifiers that routinely measure nanovolt signals. However, because of the way they work, lockin ampliﬁers achieve that bandwidth anywhere within a wide frequency range—not just near DC. At very low frequencies, thermal drift is a problem. The purpose of many experiments is to measure resistance, which generally is temperature sensitive. In addition, some materials act like current or voltage sources at a very low level so these effects must be separated from the voltage developed by the test current. To eliminate the effects of selfgenerated currents or voltages, it has become common practice to average 2 8 • E E • December 2008 successive pairs of measurements, one made with current applied in the forward direction and the other with the current reversed. A further reﬁnement uses three measurements to provide very good thermal drift cancellation. When making these measurements, it’s important to minimize the temperature change from one measurement to the next. Because of this, the speed with which a current source can be reversed or a nanovolt-level signal measured has become important. Lock-in Ampliﬁer Various datasheets refer to the development of lock-in ampliﬁers in the 1960’s. They tend to be listed under electrophysical or electrochemical equipment rather than as a general-purpose electronic measuring device. The operating principle is elegant in its simplicity. If the experiment is excited by a very pure sinewave at a single frequency, the output can be measured by a phase-sensitive detector at precisely that frequency. Equation 1 explains the process mathematically. T h e a m p l i f i e r ’s r e f e r e n c e i s , a pure sinewave at frequency and phase . The output from the experiment, a sinewave at frequency and phase with amplitude , is multiplied by the reference in the phase-sensitive detector. The output from the detector is ) In general, the output frequency is exactly the same as the exciting frequency so the cosine of the frequency difference equals 1.0. The frequency sum term is at twice the reference frequency and easily ﬁltered and eliminated. The term that remains is proportional to the experiment output signal amplitude and phase difference. A lock-in amplifier with two detectors—a dual-phase lock-in—has two references in quadrature and de- termines both the cosine of the phase difference as well as a separate sine term. In other words, it computes an in-phase and a quadrature component of the output. From these values, the resultant magnitude R can be derived. These instruments label outputs X for the real or in-phase axis, Y for the quadrature component that is 90° out of phase, and R. In theory, a lock-in ampliﬁer seems like a great idea. Today’s digital versions actually perform very well, especially in comparison to earlier analog models. Almost all of the analog circuit areas cause problems because they simply are not as precise as needed. For example, the sinewave reference generator may lack the required purity. This means that the phase detector will be sensitive to harmonics. In fact, some analog lock-in ampliﬁers use a square wave as the reference and are sensitive to all the odd harmonics of the fundamental. In contrast, a 20-bit digital sine generator might have harmonics as low as -120 dB. Preceded by a suitable amount of low-noise analog ampliﬁcation, a modern 18-b ADC introduces little noise on its own. In the Stanford Research Systems Model SR850 Digital Lockin Ampliﬁer, gain ahead of the ADC is high enough that the actual signal noise is larger than the ADC noise. The subsequent multiplication of the signal by the reference is almost perfect, being done digitally and with high resolution. Very large noise levels must be accommodated while at the same time providing enough gain to get the needed sensitivity. The ratio of the largest permitted signal to the full-scale value of a particular range is called the dynamic reserve. Digital lock-in ampliﬁers are more ﬂexible in the way gain is distributed before and after the ADC and detector. Because the SR850 performs digital multiplication and ﬁltering, large amounts of post-detector gain can be provided with few undesirable consequences. Analog detectors have a limited dynamic range, and some lock-in amwww.e v al u a ti o n e n g i n e e r i n g . c o m http://www.evaluationengineering.com

Table of Contents Feed for the Digital Edition of Evaluation Engineering - December 2008

Evaluation Engineering - December 2008 Contents Editorial Product Briefing Test Software C-V Measurements Nanoelectronics Test Product Guide Company Guide Machine Vision EMC Test Index of Advertisers

Evaluation Engineering - December 2008

For optimal viewing of this digital publication, please enable JavaScript and then refresh the page. If you would like to try to load the digital publication without using Flash Player detection, please click here.