The number of integrators, and consequently, the numbers of feedback loops, indicates the order of a ΔΣ-modulator; a 2nd order ΔΣ modulator is shown in Fig. 4. First order modulators are unconditionally stable, but stability analysis must be performed for higher order modulators.
3-level and higher quantizer[edit]
The modulator can also be classified by the number of bits it has in output, which strictly depends on the output of the quantizer. The quantizer can be realized with a N-level comparator, thus the modulator has log2N-bit output. A simple comparator has 2 levels and so is 1 bit quantizer; a 3-level quantizer is called a "1.5" bit quantizer; a 4-level quantizer is a 2 bit quantizer; a 5-level quantizer is called a "2.5 bit" quantizer.[4]
Decimation structures[edit]
The conceptually simplest decimation structure is a counter that is reset to zero at the beginning of each integration period, then read out at the end of the integration period.
The multi-stage noise shaping (MASH) structure has a noise shaping property, and is commonly used in digital audio and fractional-N frequency synthesizers. It comprises two or more cascaded overflowing accumulators, each of which is equivalent to a first-order sigma delta modulator. The carry outputs are combined through summations and delays to produce a binary output, the width of which depends on the number of stages (order) of the MASH. Besides its noise shaping function, it has two more attractive properties:
simple to implement in hardware; only common digital blocks such as accumulators, adders, and D flip-flops are required
unconditionally stable (there are no feedback loops outside the accumulators)
A very popular decimation structure is the sinc filter. For 2nd order modulators, the sinc3 filter is close to optimum
The number of integrators, and consequently, the numbers of feedback loops, indicates the order of a ΔΣ-modulator; a 2nd order ΔΣ modulator is shown in Fig. 4. First order modulators are unconditionally stable, but stability analysis must be performed for higher order modulators.
3-level and higher quantizer[edit]
The modulator can also be classified by the number of bits it has in output, which strictly depends on the output of the quantizer. The quantizer can be realized with a N-level comparator, thus the modulator has log2N-bit output. A simple comparator has 2 levels and so is 1 bit quantizer; a 3-level quantizer is called a "1.5" bit quantizer; a 4-level quantizer is a 2 bit quantizer; a 5-level quantizer is called a "2.5 bit" quantizer.[4]
Decimation structures[edit]
The conceptually simplest decimation structure is a counter that is reset to zero at the beginning of each integration period, then read out at the end of the integration period.
The multi-stage noise shaping (MASH) structure has a noise shaping property, and is commonly used in digital audio and fractional-N frequency synthesizers. It comprises two or more cascaded overflowing accumulators, each of which is equivalent to a first-order sigma delta modulator. The carry outputs are combined through summations and delays to produce a binary output, the width of which depends on the number of stages (order) of the MASH. Besides its noise shaping function, it has two more attractive properties:
simple to implement in hardware; only common digital blocks such as accumulators, adders, and D flip-flops are required
unconditionally stable (there are no feedback loops outside the accumulators)
A very popular decimation structure is the sinc filter. For 2nd order modulators, the sinc3 filter is close to optimum
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