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.