This work presents a new method to estimate the nonlinearity characteristics of analog-to-digital converters (ADCs). The method is based on a nonnecessarily polynomial continuous and differentiable mathematical model of the converter transfer function, and on the spectral processing of the converter output under a sinusoidal input excitation. The simulation and experiments performed on different ADC examples prove the feasibility of the proposed method, even when the ADC nonlinearity pattern has very strong discontinuities. When compared with the traditional code histogram method, it also shows its low cost and efficiency since a significant lower number of output samples can be used still giving very realistic INL signature values.

The parameters that characterize the transfer function of an ADC, such as the integral
nonlinearity (INL), are some of the most important specifications that must be
known to insure the correct operation of the ADC in a certain application. One
of the standardized methods to estimate these parameters is the code histogram test
[

These drawbacks make the histogram method
unfeasible for low-speed and high-resolution converters (>15 bits). For
these kinds of converters, the use of methods based on spectral processing can
be satisfactory acquiring only some tens of thousands of samples independently
of the ADC resolution [

This paper presents a new and simple method for
ADC nonlinearity (INL) estimation using the spectral processing of its response
to a sine-wave excitation. The method does not require a concrete functional
form for the ADC transfer curve or for the INL, as [

The organization of this paper is as follows.
Section

The ADC basic model that we are considering supposes that the transfer curve: (1) is a smooth nonnecessarily polynomial function

Mathematically, the proposed input-output model
is

Figure

Modelling the non-linearity: the first order Taylor’s expansion of the transfer function

From (

If the second derivative exists, an alternative
expression can be obtained using the second-order Taylor’s expansion. In any case, in this work
only the expression (

This section shows how to apply expression (

Let us assume that the input excitation is

For such input, the ADC output is a
superposition of harmonics of the excitation frequency,

Now, let us evaluate expressions (

If

Defining the input wave crossing points

The number of harmonics
that must be selected to apply (

In very good coherent
experiments (input frequency and sampling frequency are commensurable values),
and when the noise is small enough and well described by additive white model,
simple relationships can be used. Being acquired

Although it has been
suggested about (

If

If a coherent sampling is not possible,

When high-order harmonics exist and they are
folded in the

The DC component is evaluated by means of the
weighted mean of the samples, using as weight function the convolution window,

This section shows the simulation results obtained applying the introduced method in
two different models for the ADC. The first converter, AD

Before applying (

AD

On the other hand, it has been applied the
standard sinusoidal histogram method [

(a) INL estimates of the example AD

Figure

For the same AD

(a) Typical averaged magnitude spectrum obtained from the AD

(a) Overlapped AD

The AD

The phase has been evenly spread allover the
experiments inside the range

The so irregular and discontinuous structure of
the INL of this ADC leads to a typical selection about 150 harmonics with
orders up to 600th. Figure

(a) Comparison between two AD

(a) Thick (black) line: estimated AD

This section shows the results obtained applying the introduced method to a real ADC. This converter has a transfer curve with very strong discontinuities.

The ADC under test is a
fully differential 12-bit pipeline converter prototype in a 120 nm CMOS
technology with reference voltages −1 V and 1 V. The sinusoidal input has been nonbuffered
AC coupled to the ADC and generated using the Agilent N8241A AWG, with amplitude
of −0.1 dBFS and a frequency of 500 kHz approximately. In this case, as a good
coherent experiment has been done, only a register of 4090 samples has been
acquired using a 20 MHz sampling master clock (neither averaging nor windowing has been applied).
Figure

(a) Typical magnitude spectrum obtained from the prototype Pipeline ADC output.
(b) Comparison between two INL estimations: In thin (blue) line, the

Figure

In this paper, a new method for the INL estimation of ADCs has been presented which is based on a continuous model of the ADC transfer function. The method uses a spectral processing of the ADC output to estimate its harmonic amplitudes and phase-shifts from which the INL signature is derived. Different ADC examples with very different nonlinearity pattern have been performed to validate the proposed method. The obtained results have been compared with those obtained from the traditional histogram method and have proven not only the feasibility of the new method, even when the ADC nonlinearity has very strong discontinuities, but also its low cost and efficiency since a significant lower number of output samples can be used still giving very realistic INL signature values.

The authors would like to thank Jesús Ruiz and Dr. Manuel Delgado, both from
Microelectronic Institute of Seville, to allow the application of our method to
their prototype ADC exposed in Section