Coded data generation or conversion – Analog to or from digital conversion – Differential encoder and/or decoder
Reexamination Certificate
2002-01-31
2004-12-14
Wamsley, Patrick (Department: 2819)
Coded data generation or conversion
Analog to or from digital conversion
Differential encoder and/or decoder
C341S155000
Reexamination Certificate
active
06831577
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to a method for designing a sigma delta modulator (SDM). Furthermore, the present invention relates to a SDM having an enlarged maximum dynamic range compared to conventional SDM. Even further, the present invention relates to microphone modules, hearing aids, cellular phones and head-sets comprising a SDM according to the present invention.
BACKGROUND OF THE INVENTION
SDMs have received much attention in recent years. The combination of over-sampling and noise shaping has revealed performance levels, which were not achievable just a years ago in integrated circuit technology. The principle can be used in many applications. Examples such as analog to digital converters, digital to analog converters, phase locked loops, PDM systems, PWM systems etc. have proven the versatility of this principle. The basic idea is that clock frequency is traded off for resolution.
A generic model (purely mathematical description) of a SDM shown in
FIG. 1
, consists of a pre-filter
101
, a feedback filter
102
and a quantizer
103
. The pre-filter and the feedback filter have the transfer-functions G(z) and H(z). To obtain a linear model of the modulator the quantizer is replaced by a linear gain block
104
, and a noise source
105
. The gain block has a gain of k. This model allows us to use all the standard mathematical tools available for linear systems for analysing the SDM.
To characterize the SDM two transfer functions are defined. These are the Signal Transfer Function (STF) and the Noise Transfer Function (NTF). The STF is defined as the transfer-function from the input of the modulator to the output. And the NTF is defined as the transfer-function from the quantization noise source to the output.
The two transfer functions are given by:
S
T
F
k
=
k
·
G
(
z
)
1
+
k
·
H
(
z
)
N
T
F
k
=
1
1
+
k
·
H
(
z
)
Where k is the equivalent linear gain of a comparator.
A specific group of SDM, which are of special interest, is one bit single loop SDM. This type of SDMs have the advantage of being especially easy to implement in integrated circuit technology, and especially for low voltage applications the very simple implementation is advantageous.
One bit single loop SDMs comprise a plurality of integrators embedded in a feedback loop with a plurality of feedback branches. This topology forms the feedback filter
102
and the pre-filter
101
. It can be shown that the NTF is a high pass filter function while the STF is a low pass filter-function. I.e. the quantization noise is suppressed at low frequencies while the low frequency input signal is passed unaffected through the modulator. A subsequent filter, digital or analog, can then remove the high frequency noise thus leaving the low frequency part of the signal with an improved signal to noise ratio.
When designing a SDM it is the design of the filter, which influences the performance of the SDM. It is of interest to choose the order and the coefficients of the filter in such a way that the noise is minimized in the frequency range of interest.
It is advantageous to design the NTF as a Butterworth filter as it has a low sensitivity to coefficient variations. A simplified Butterworth NTF is shown in FIG.
2
. If the frequencies below the broken line
203
in the output of the SDM are the most important (such as in audio applications), then the NTF should suppress the lower frequency noise as much as possible. This can be achieved in two ways, either
1. by increasing the order of the filter and thereby increase the slope
205
of the noise transfer, or
2. by increasing the cut-off frequency
201
.
For a filter of a given order, the only choice available is the choice of having a NTF with a very high cut-off frequency. However, there is an upper limit how much the cut-off frequency of the NTF can be increased. Increasing the cut-off frequency results in that the maximum stable amplitude (MSA) of the input signal decreases. All higher order SDM's have the property that when the input signal's amplitude exceeds a certain MSA value the SDM becomes unstable and starts to oscillate. The definition of a higher order SDM is that the number of integrators in the loop is larger than two.
To summarize, the trade-offs when choosing the cut-off frequency in the NTF are:
high cut-off frequency results in less noise and a lower MSA.
whereas
low cut-off frequency results in more noise and higher MSA.
According to the above, it is therefore of interest to design the filter in such a way that the optimal cut-off frequency is chosen—meaning a cut-off frequency resulting in maximum MSA vs. noise ratio—i.e. maximum signal to noise ratio (SNR
max
). For each order of SDM's and NTF filter function an optimum NTF cut-off frequency exists for which the SNR
max
is maximized.
The modulator has to be capable of handling input signals larger than the MSA. A typical way of assuring stability of the modulator is to reset the integrators of the modulator when the amplitude of the input signal exceeds MSA. Instability can also be detected by monitoring the output signal, or it can be detected by monitoring, independently, the output signals of each integrator, and then resetting the integrators accordingly.
The above-mentioned way of accounting for instability is very effective, but unfortunately, it also introduces distortion in the output signal when the integrators are reset. An alternative way of ensuring stability is to limit the output swing of the integrators so that the signal swing at the output of each integrator do not increase uncontrollable—even in the situation when the input signal exceeds MSA causing the modulator to become unstable. This approach is very attractive as it introduces minimum distortion and gives a large dynamic range (DNR). Unfortunately, this approach is very difficult to implement in low voltage circuit design.
It is therefore of interest to establish a new and optimized design route for SDMs to ensure maximum DNR and stability while keeping the distortion in the output signal at a minimum for input signals exceeding MSA.
The dynamic range is defined as the ratio between the maximum output signal power and the output idle (no input signal) noise power.
When designing SDMs for use in low power/low voltage applications a variety of factors have to be taken into consideration since the implementation is not ideal compared to an ideal SDM. Examples of this being: non-infinite gain of integrators, circuit noise etc.
It is an object of the present invention to provide a new and optimized design route for SDMs for low power and low voltage applications to ensure maximum DNR, maximum SNR
max
and maximum stability.
SUMMARY OF THE INVENTION
The above-mentioned object is complied with by providing, in a first aspect, a method for designing a sigma-delta-modulator comprising a plurality of cascaded integrators and a comparator, the method comprising the steps of:
providing an input signal to an input of the sigma-delta-modulator,
determining an amplitude of a signal at an output of at least one of the plurality of integrators,
adjusting the signal swing of the output signals of those of the integrators being placed closest in the signal path to the input of the sigma-delta-modulator by adjusting characteristics of those integrators in such a way that the signal swing of those integrators being placed closest to the input is significantly smaller than the signal swing of the remaining integrators.
By cascaded integrators is meant that an integrator output is connected to the input of a following integrator. An integrator can in an embodiment be realized using digital or analog electronics.
A comparator is a component transforming the amplitude continuous input signal to an amplitude discrete output signal having either a first or a second value. The input of the SDM may be the input of the first integrator in the cascade of integrators.
Typically, the output
Harness Dickey & Pierce PLC
Sonion A/S
Wamsley Patrick
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