Hello. And welcome to the TI Precision Lab introducing AC and DC Specifications. Precision Labs is a comprehensive online curriculum for analog engineers. More videos can be found by going to TI.com/PrecisionLabs. In this video, we'll define offset error, gain error, common mode rejection ratio, and power supply rejection ratio. We will also give a brief introduction to the AC specifications of signal to noise ratio and total harmonic distortion.

Let's start with the basic calculation for offset and gain error. The key to understanding this is to know that the ADC transfer function is not perfectly linear. So a linear fit curve is applied to the function. For this calculation, the most commonly used type of curve fit is an endpoint linear fit. With this type of curve fit, the first and last points on the ADC transfer function define the straight line.

Recall that a straight line has the equation y equals mx plus b. Also the slope can be calculated by taking the change in y divided by the change in x. Sometimes this is referred to as the rise over run.

The offset is the Y-axis intercept. That is, the offset is the value of the transfer function when x equals 0. This value can be calculated by rearranging the equation y equals mx plus b and solving for b where b is the offset.

The gain error is the percentage difference between the ideal slope and the measured slope. The gain error and offset error are often referred to as DC errors, as they can be measured with DC input signals plot.

Let's take a closer look at offset error. Here we introduce the concept of common mode rejection and power supply rejection. The common mode voltage is the average voltage applied to both inputs. As this input changes, it will introduce an error source that can be modeled as an offset voltage source on the ADC input VCM error. The magnitude of this error source can be determined using the common mode rejection ratio, or CMRR, specification.

CMRR is usually specified in decibels and can be calculated by taking negative 20 times the log of the change in common mode error divided by the change in common mode voltage. This equation can be rearranged to solve for the change in common mode error based on the change in common mode voltage.

Power supply rejection, or PSRR, also generates an error source in series with the ADC input. Power supply rejection error is a function of the change in the power supply voltage. Variations or noise on the power supply will reflect back to the input as an error source. The equation for power supply rejection is the same form as the common mode rejection. But in this case, it is based on power supply variations. Again, this can be rearranged to solve for the change in power supply rejection error based on the change in supply voltage. We will take a closer look at CMRR and PSRR in the next few slides.

This slide shows an example of an ADC's common mode rejection specification. A simple way to test common mode rejection is to connect the two inputs together and sweep the common mode voltage. Remember that common mode voltage is the average of the voltage on the two inputs. So when the inputs are tied together the input signal is the common mode voltage.

In this example, if we want to sweep the common mode voltage from 5 volts to 2 and 1/2 volts, the change in common mode voltage is 2 and 1/2 volts. Substituting these numbers into the common mode rejection equation, we can see that the common mode error is 25 microvolts.

Power supply rejection looks at the air introduced by a change in the power supply voltage. This shift can be a DC change in the supply voltage, or it may be a noise signal. For this example, let's consider a 200-millivolt peak to peak 200-kilohertz noise signal on the supply. Normally, the specification listed in the datasheet table is the PSRR for DC changes in the power supply voltage. For the PSRR over frequency, a bully plot may be shown in the characteristic curves section.

In this example, we can find that the PSRR is 58 dB at 200 kilohertz. Using the PSRR Equation introduced earlier, we can determine the error introduced by the power supply rejection. Plugging the 200-millivolt peak to peak and 58 dB into the equation yields a noise of 252 microvolts peak to peak.

Let's move on to the next specification. This slide shows the general equation for a data converter's signal to noise ratio or SNR. In general, the signal to noise ratio is a measurement of how clean or noise-free a signal is. A high SNR indicates that the signal is very large in comparison to the noise, whereas a low SNR indicates that the noise is high relative to the signal.

For this specification, both the noise and signal are measured and volts RMS. So you need to take 20 times the log of the ratio to convert it to decibels. The ideal SNR in decibels can be calculated by taking 6.02 times n plus 1.76 where n is the number of bits of resolution of the ADC. A 10-bit converter, for example, would have 6.02 times 10 plus 1.76 or 61.96 decibels.

This relationship was derived by integrating the quantization noise and applying the signal to noise relationship. This relationship is true for an ideal converter where the only error source considered is quantization noise. No practical data converter will ever have a better signal to noise than what is given by this equation, because practical converters have other noise sources.

Another common AC specification is total harmonic distortion or THD. In order to understand THD, it is important to understand nonlinearity. Nonlinearity is a measurement of how much a transfer function deviates from its ideal straight line. The transfer function shown on the left-hand side of the slide shows an ideal linear transfer function and a nonlinear transfer function. The ideal transfer function follows a straight line in the form y equals mx plus b, whereas the nonlinear transfer function will have higher order terms causing deviations from the line.

The nonlinear example shown is exaggerated to make the nonlinearity easy to see. Notice how the nonlinear function tracks well for low-input voltage levels and deviates as the input increases. In short, the gain for higher-input signals is larger than it should be. This has the effect of stretching out the top half cycle of the sine wave. This stretching of the top half cycle is called distortion and will create harmonics in the frequency spectrum.

This slide shows the frequency spectrum for the digitized sine wave at the right. The harmonics are a result of the distortion on the top half cycle of the waveform. Harmonic distortion will always occur at integer multiples of the fundamental frequency. In this case, the fundamental is at 1 kilohertz, and there are harmonics at 2 kilohertz, 3 kilohertz, 4 kilohertz, and so on.

Sometimes, it is useful to differentiate between even and odd harmonics, as different circuit non-idealities may generate one type of harmonic. Even harmonics are even multiples of the fundamental frequency. And odd harmonics are odd multiples of the fundamental. For example 2 kilohertz and 4 kilohertz are even harmonics, whereas 3 kilohertz and 5 kilohertz are odd harmonics. If the digitized signal perfectly tracked the input signal, there would not be any harmonics.

The THD calculation is given here as a percentage as well as in decibels. The IEEE standard for ADC testing specifies that nine harmonics should be used in the THD calculations. THD is the square root of the sum of the harmonic voltages squared divided by the RMS signal voltage squared. This quantity is multiplied by 100 to convert to a percentage, or 20 times the log is taken to convert to decibels.

THD plus N is similar to THD, except that it includes the total RMS noise in the calculation. SINAD is short for signal to noise and distortion. Mathematically, SINAD is simply the reciprocal of the THD plus N calculation. In decibels, taking the reciprocal will just change the sign of the number. Note that SINAD or THD plus N will always be worse than either the THD or SNR, because SINAD is really a combination of the two error sources.

That concludes this video. Thank you for watching. Please try the quiz to check your understanding of this video's content.