Coded data generation or conversion – Analog to or from digital conversion – Differential encoder and/or decoder
Reexamination Certificate
2002-12-23
2004-09-21
Toker, Michael (Department: 2819)
Coded data generation or conversion
Analog to or from digital conversion
Differential encoder and/or decoder
C341S155000
Reexamination Certificate
active
06795002
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to gain scaling of multistage, multi-bit delta sigma modulators for higher signal-to-noise ratios.
2. Background Art
Commercialization of the Internet has proven to be a mainspring for incentives to improve network technologies. Development programs have pursued various approaches including strategies to leverage use of the existing Public Switched Telephone Network and plans to expand use of wireless technologies for networking applications. Both of these approaches (and others) entail the conversion of data between analog and digital formats. Therefore, it is expected that analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) will continue to perform critical functions in many network applications.
FIG. 1
shows a process for converting an analog signal “x[n]”
102
to a digital signal “z[n]”
104
using an exemplary ADC
106
. ADC
106
receives analog signal x[n]
102
and produces digital signal z[n]
104
. Analog signal x[n]
102
comprises variations of a parameter (e.g., voltage) continuously with time. The variations in the parameter of analog signal x[n]
102
are maintained within a range between a lower value “LOW”
108
and a higher value “HIGH”
110
. This is referred to as the “swing” of analog signal x[n]
102
. Typically, analog signal x[n]
102
is characterized by a carrier frequency. Digital signal z[n]
104
comprises a sequence of discrete quantized values that, over time, tracks the parameter variations of analog signal x[n]
102
. Typically, the quantized values of digital signal z[n]
104
are represented by binary numbers. A maximum value “MAX”
112
is defined by the number of different quantized values that can be produced by ADC
106
.
FIG. 2
is a block diagram of ADC
106
. ADC
106
comprises a sampling functional component
202
and a quantization functional component
204
. Sampling functional component
202
records, at a sampling frequency, discrete values of analog signal x[n]
102
. Typically, the sampling frequency is greater than or equal to the Nyquist frequency, which is twice the carrier frequency of analog signal x[n]
102
. Quantization functional component
204
assigns a quantized value to represent each discrete sampled value, thereby producing digital signal z[n]
104
.
The difference between digital signal z[n]
104
and analog signal x[n]
102
is referred to as quantization error e[n]. Ideally, there is a direct relationship between the values of analog signal x[n]
102
and digital signal z[n]
104
at corresponding points in time. In reality, the use of a limited number of quantized values for digital signal z[n]
104
dictates that, in some instances, values of analog signal x[n]
102
must be approximated. It is desirable to minimize quantization error e[n], which is an unwanted byproduct of the quantization process.
FIG. 3
illustrates the process within quantization functional component
204
. The range of parameter variations of analog signal x[n]
102
is divided into a number of equal-sized subranges. The number of equal-sized subranges is defined by the value of MAX
112
. If, for example, MAX
112
equals four, then the range of parameter variations of analog signal x[n]
102
is divided into four subranges, each measuring one-quarter of the range between LOW
108
and HIGH
110
. A subrange “A”
302
extends from LOW
108
to a value at a point “Q
1
”
304
. A subrange “B”
306
extends from Q
1
304
to a value at a point “Q
2
”
308
. A subrange “C”
310
extends from Q
2
308
to a value at a point “Q
3
”
312
. A subrange “D”
314
extends from Q
3
312
to HIGH
110
.
Both analog signal x[n]
102
and digital signal z[n]
104
are usually biased by specific values that can obscure the underlying relationship between the two signals. This relationship is more readily explained when analog signal x[n]
102
is understood to be centered at a point measuring one-half of the range between LOW
108
and HIGH
110
. In the present example, this point is Q
2
308
. By translating the actual value of Q
2
308
to zero and the remaining points in analog signal x[n]
102
accordingly, the bias value is removed from analog signal x[n]
102
. Therefore, quantized values derived from this translated analog signal x[n]
102
correspond to digital signal z[n]
104
with its bias value removed.
FIG. 9
is a graph
900
of bias-free values of quantized signal y[n]
828
, produced by single-bit quantizer
814
, as a function of bias-free values of analog signal x[n]
102
. With analog signal x[n]
102
centered at a point measuring one-half of the range between LOW
108
and HIGH
110
(e.g., point Q
2
308
from the example above), quantizer
814
divides analog signal x[n]
102
into two subranges. Quantizer
814
assigns a lower value “LOWER”
902
to those values of analog signal x[n]
102
that are less than the midpoint (e.g., Q
2
308
) value, and a higher value “HIGHER”
904
to those values of analog signal x[n]
102
that are greater than the midpoint (e.g., Q
2
308
) value. Typically, LOWER
902
is the lowest quantized value and HIGHER
904
is the highest quantized value that can be produced by quantizer
814
.
The number of subranges determines the degree of resolution of ADC
106
. Degree of resolution is typically expressed as the number of binary digits (i.e., bits) in the quantized values that can be produced by ADC
106
. ADC
106
is characterized by its sampling frequency and its degree of resolution. The ability of ADC
106
to digitize analog signal x[n]
102
faithfully is a direct function of both of these. As the sampling frequency is increased, analog signal x[n]
102
is sampled at more points in time. As the degree of resolution is refined, the differences between digital signal z[n]
104
and analog signal x[n]
102
are minimized.
FIG. 4
is a graph
400
of bias-free values of digital signal z[n]
104
as a function of bias-free values of analog signal x[n]
102
. A dashed line
402
represents the ideal direct relationship between the values of analog signal x[n]
102
and digital signal z[n]
104
. The slope of dashed line
402
corresponds to the gain of ADC
106
. A shaded portion
404
between graph
400
and dashed line
402
corresponds to quantization error e[n]. The same error pattern applies to each subrange. The measure of each subrange is referred to as the measure of a Least Significant Bit (LSB).
Statistical methods are often used to analyze quantization error e[n].
FIG. 5
is a graph
500
of a probability density “P(p)”
502
of a subrange of digital signal z[n]
104
as a function of the parameter “p”
504
of analog signal x[n]
102
. Probability density P(p)
502
is centered at the midpoint of the subrange (i.e., at a
316
, b
318
, c
320
, or d
322
). Probability density P(p)
502
corresponds to quantization error e[n]. Probability density P(p)
502
shows that digital signal z[n]
104
has the same value throughout the subrange, where the subrange extends on either side of its midpoint for a measure equal to one-half of the LSB. The constant value of digital signal z[n]
104
within each subrange and its relation ship to quantization error e[n] is also shown by graph
400
.
Further analysis of quantization error e[n] is often performed in the frequency domain.
FIG. 6
is a graph
600
of probability density P(p)
502
in the frequency domain. Graph
600
shows an “absolute value of p”
602
as a function of frequency “freq”
604
. In the fre
Broadcom Corporation
Nguyen Khai
Sterne Kessler Goldstein & Fox P.L.L.C.
Toker Michael
LandOfFree
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