Optically sampled delta-sigma modulator

Details Optically sampled delta-sigma modulator Optically sampled delta-sigma modulator

2002-10-25

2004-08-24

Young, Brian (Department: 2819)

Coded data generation or conversion

Analog to or from digital conversion

Differential encoder and/or decoder

C341S144000

Reexamination Certificate

active

06781533

ABSTRACT:

FIELD OF THE INVENTION
This invention relates to optically sampled delta-sigma analog-to-digital converters and more specifically to an optically sampled delta-sigma modulator.
BACKGROUND OF THE INVENTION
It has been known for many years that delta-sigma modulation techniques can be used in analog-to-digital (A/D) converters. Only recently, however, have these techniques achieved widespread popularity. This popularity can be attributed to advances in VLSI technology that have allowed the realization of densely packed high speed circuits that are capable of effectively handling the bit stream associated with delta-sigma modulation.
A typical delta-sigma converter
100
is shown in
FIG. 1A
, and comprises a delta-sigma modulator
102
and a digital low-pass decimation filter
104
. The delta-sigma modulator
102
comprises a summing node
111
, an integrator
113
and a quantizer
115
coupled together in succession. A feedback loop
117
couples the output Y(i) of the delta-sigma modulator to the summing node
111
through a digital-to-analog (D/A) converter
112
. In operation, an analog input signal that has been sampled X(i) enters the summing node
111
where an analog version of the feedback signal Y
a
(i) is subtracted from X(i) to create a difference signal X
d
(i). The difference signal X
d
(i) is then input to the integrator
113
, which produces an integrated signal X
i
(i). The quantizer then rounds the integrated signal X
i
(i) to a closest possible level thereby producing a digital signal Y(i). The feedback loop
117
forces the average output of the modulator to be equal to the input signal X(i). The digital decimation filter
104
then processes the output stream of the delta-sigma modulator.
One byproduct of A/D conversion is quantization error. Quantization error occurs because the magnitude of the analog signals entering the quantizer can theoretically be equal to an infinite number of values, whereas the magnitude of the rounded signals leaving the quantizer can only be equal to a finite number of values. Therefore, the quantizer causes a rounding off, or quantization error.
The advantage of delta-sigma converters is their ability to reduce, relative to other types of converters, quantization error through the use of noise shaping and oversampling. Noise shaping is a filtering operation performed by the integrator
113
and feedback loop
117
that pushes the noise caused by the quantization error outside the bandwidth of interest. Oversampling performs the initial sampling operation at a rate much higher than twice the signal frequency. Then, when the quantized signal is processed by a lowpass decimation filter, much of the noise pushed to higher frequencies is removed by the filter.
Noise shaping will now be described with reference to the Z transform model of the delta-sigma modulator
102
shown in FIG.
1
B. The integrator
113
, often called the “feed forward loop filter,” is a discrete time integrator having a transfer function of Z
−1
/(1−Z
−1
). Since the quantization noise is random, the quantizer
115
can be modeled as a noise source N(Z) coupled to a summing node
119
. Moreover, the D/A converter
112
can be treated as ideal, and modeled as a unity gain transfer function for a single bit D/A converter. The output of the modulator is then given by:
Y(Z)=X(Z)Z
−1
+N(Z)(1−Z
−1
)
Thus, the transfer function for the input signal, H
x
(Z), is equal to Z
−1
, and the transfer function of the noise source, H
n
(Z), is equal to (1−Z
−1
). Since zero frequency is represented in the Z transform at Z=1, it can readily be seen that, as the frequency approaches zero, N(Z) is attenuated. Therefore, the delta-sigma modulator acts as a high pass filter for quantization noise, and a low pass filter for the input signal.
The second way that delta sigma modulators reduce quantization noise is through oversampling. It is well known that to recover a sampled analog signal, the signal must be sampled at a rate greater than or equal to twice the signal frequency. Oversampling refers to sampling the signal at a rate much greater than twice the signal frequency.
FIG. 2A
shows the magnitude of quantization noise, in terms of the signal-to-noise ratio (SNR), at a particular frequency of interest f when the analog signal is sampled at the minimum sampling rate of f
s
.
FIG. 2B
shows the magnitude of quantization noise at the same frequency of interest f when the signal is sampled at a sampling rate equal to 2f
s
. By comparing the quantization noise in
FIGS. 2A and 2B
, respectively, one can see that increasing the sampling frequency spreads the quantization noise over a larger bandwidth because the total amount of quantization noise remains the same over the different sampling bandwidths. Thus, increasing the sampling rate relative to twice the signal frequency, or oversampling, reduces the quantization noise in the bandwidth of interest.
One factor that limits the performance of analog-to-digital converters is temporal jitter in the sampling clock. Sampling clock jitter results in non-uniform sampling and increases the total error power in the quantizer output. If the clock jitter is assumed to contribute white noise, the total power of the error is reduced in a delta-sigma A/D converter by the oversampling ratio. Nevertheless, the clock jitter still can be a limiting factor for conversion of wideband signals.
One way to overcome sampling jitter limitations is through optical sampling. Optical sampling makes use of very short laser pulses with high temporal stability to sample an analog electrical input. Subpicosecond sampling, or aperture windows and sampling-pulse repetition rates above 40 GHz, can be achieved with optical sampling. The jitter of the optical sampling pulses can be less than 10 fsecs.
A conventional optically sampled A/D converter
200
is shown in
FIG. 3. A
series of optical impulses
201
from a mode-locked laser
203
are applied to an electro-optic modulator
205
. The analog electrical input X(t) is also applied to the modulator
205
. The optical impulses
201
sample the voltage associated with the analog electrical input X(t). The resultant optical pulses
207
, with intensities determined by the modulator
205
voltage, are fed to a photodetector
209
. The photodetector
209
electrical output
211
is supplied as the input of an electronic quantizer
212
.
The above approach achieves very high sampling rates because the pulse repetition rate of the mode-locked laser can be 40 GHz or higher. Even higher repetition rates for the optical sampling pulses can be achieved by combining several time-delayed copies of each laser pulse.
A photonic sampler can be combined with a discrete-time delta-sigma modulator, as illustrated in
FIG. 3
, by replacing the electronic quantizer
212
with such a discrete-time modulator. Typical discrete-time delta-sigma modulators are implemented as switched-capacitor networks, since these circuits provide good control and flexibility in the realization of the noise-shaping and signal-transfer functions. The sampling rate of such switched-capacitor implementations, however, is limited to one-half or less of the unity gain bandwidth of its operational amplifiers. Also, such implementations typically are compatible only with CMOS transistor technologies.
For high sampling rates, continuous-time delta-sigma modulators are used. The sampling rates of such modulators can be greater than the unity gain bandwidth of its integrators. Also, such continuous-time modulators can be implemented in high speed transistor technologies such as heterojunction bipolar transistors formed in InP or GaAs materials. In a typical continuous-time delta-sigma modulator, the sampling occurs at the quantizer. A typical quantizer consists of an electronic latched comparator, which acts as a track and compare amplifier. In such an implementation, the sampling interval can depend on the input signal to the quantizer. The minimum sampling interval can be considered to

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