Delta-sigma modulation

Modifying the delta modulator into a sigma-delta modulator can eliminate the above problems. The development of sigma-delta modulation SDM began in the s, to overcome the limitations of delta simulation. Sigma-delta systems quantize the delta D, difference between the current sigma and the sigma sum of the previous difference it is a closed loop feedback system. An integrator is placed at the input of the quantizer; the signal amplitude is constant at a varying frequency similar to frequency modulation, FM.

Thus the quantization range is dependent upon the maximum signal amplitude and not on the signal spectrum. To achieve high resolution as in the PCM high sampling rates are required. For instance, in CD players with a maximum allowable input signal of 20kHz In this way quantization noise is spread from dc 0Hz to kHz 16 x 20kHz.

SDM adds noise-shaping benefits as the integrator "kills" high frequency noise. Figure 6 shows a first order single integrator SDM encoder. The input to the quantizer is the integral of the difference between the input and the quantized output. The difference between the input signal and the output signal approaches zero; the average value of the clocked output tracks the input. The integrator forms a low-pass filter on the difference signal thus providing low frequency feedback around the quantizer.

This feedback results in a reduction of quantization noise at low in-band frequencies. In practice, the in-band noise floor level is not satisfactory with first-order SDM. Considering the same example as in the delta modulator case, that is 1. The same audio quality can thus be achieved with a lower bit conversion, something that seems unrealizable at the first glance as with fewer quantization levels the effect of noise can be more significant as it is spread over fewer bits in the audio pass-band noise carries more "weight" to the overall signal amplitude.

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However using a high enough sampling rate low-bit conversion, the in-band noise can be better attenuated or shaped-out from the audio frequency band that can even exceed the noise immunity that the strict Nyquist-rate sampling offers PCM.

The latest CD audio technology uses SDM DAC converters to convert the bits stored in a compact disc to an analog signal that we can hear through a loudspeaker. The The advantage of using a 1-bit converter in CD audio technology is that it offers better tolerance for small variances in the components that is uses against the more complex, harder to implement multi-bit decoders and encoders which use a complex inner structure of voltage references using a network of resistors as described earlier.

Since there are so many components, the variance of the value of one component affects the other components as they form a "chain" thus affecting the overall performance and audio quality reproduction. Another matter of concern is the cost: 1-bit converters offer a better cost to performance ratio to multi-bit converters they can even offer better performance at a lower cost!The sampling rate of a signal should be higher than the Nyquist rate, to achieve better sampling.

If this sampling interval in Differential PCM is reduced considerably, the sampleto-sample amplitude difference is very small, as if the difference is 1-bit quantizationthen the step-size will be very small i. As the sampling interval is reduced, the signal correlation will be higher.

delta sigma modulation

The Delta Modulator comprises of a 1-bit quantizer and a delay circuit along with two summer circuits. Following is the block diagram of a delta modulator. The output quality of the waveform is moderate. The delta demodulator comprises of a low pass filter, a summer, and a delay circuit. The predictor circuit is eliminated here and hence no assumed input is given to the demodulator. A binary sequence will be given as an input to the demodulator. The stair-case approximated output is given to the LPF.

Low pass filter is used for many reasons, but the prominent reason is noise elimination for out-of-band signals.

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The step-size error that may occur at the transmitter is called granular noisewhich is eliminated here. If there is no noise present, then the modulator output equals the demodulator input.

In digital modulation, we have come across certain problem of determining the step-size, which influences the quality of the output wave. A larger step-size is needed in the steep slope of modulating signal and a smaller stepsize is needed where the message has a small slope.

The minute details get missed in the process. So, it would be better if we can control the adjustment of step-size, according to our requirement in order to obtain the sampling in a desired fashion. This is the concept of Adaptive Delta Modulation. The gain of the voltage controlled amplifier is adjusted by the output signal from the sampler. The amplifier gain determines the step-size and both are proportional.It is also used to convert high bit-count, low-frequency digital signals into lower bit-count, higher-frequency digital signals as part of the process to convert digital signals into analog as part of a digital-to-analog converter DAC.

In a conventional ADC, an analog signal is sampled with a sampling frequency and subsequently quantized in a multi-level quantizer into a digital signal. This process introduces quantization error noise.

The first step in a delta-sigma modulation is delta modulation. In delta modulation the change in the signal its delta is encoded, rather than the absolute value. The result is a stream of pulses, as opposed to a stream of numbers as is the case with pulse code modulation PCM.

In delta-sigma modulation, accuracy of the modulation is improved by passing the digital output through a 1-bit DAC and adding sigma the resulting analog signal to the input signal the signal before delta modulationthereby reducing the error introduced by the delta modulation. A delta-sigma ADC first encodes an analog signal using high-frequency delta-sigma modulation, and then applies a digital filter to form a higher-resolution but lower sample-frequency digital output.

A delta-sigma DAC encodes a high-resolution digital input signal into a lower-resolution but higher sample-frequency signal that is mapped to voltagesand then smoothed with an analog filter. In both cases, the temporary use of a lower-resolution signal simplifies circuit design and improves efficiency.

Primarily because of its cost efficiency and reduced circuit complexity, this technique has found increasing use in modern electronic components such as DACs, ADCs, frequency synthesizersswitched-mode power supplies and motor controllers. Delta-sigma modulation converts an analog voltage signal into a pulse frequency, or pulse density, which can be understood as pulse-density modulation PDM.

Delta Modulation

A sequence of positive and negative pulses, representing bits at a known fixed rate, is very easy to generate, transmit, and accurately regenerate at the receiver, given only that the timing and sign of the pulses can be recovered. Given such a sequence of pulses from a delta-sigma modulator, the original waveform can be reconstructed with adequate precision. In contrast, without conversion to a pulse stream but simply transmitting the analog signal directly, all noise in the system would be added to the analog signal, reducing its quality.

The use of PDM as a signal representation is an alternative to pulse-code modulation PCMsampling and quantizing to a multi-bit code at the Nyquist rate. At each step a pulse is added to the pulse stream. For the purpose of introduction, Figure 1 illustrates the concept of voltage-to-frequency conversion, in an unclocked form that resembles delta-sigma modulation, and is called asynchronous modulation [2]asynchronous delta-sigma modulation[3] [4] or free-running modulators.

Shown below that are waveforms at points designated by numbers 1 to 5 for an input of 0. The stream of delta impulses generated at each threshold crossing is shown at 2 and the difference between 1 and 2 is shown at 3. This difference is integrated to produce the waveform 4. The threshold detector generates a pulse 5 which starts as the waveform 4 crosses the threshold and is sustained until the waveform 4 falls below the threshold.

The threshold 5 triggers the impulse generator to produce a fixed-strength impulse. The integral 4 crosses the threshold in half the time in the right column than in the left column. Thus the frequency of impulses is doubled. Hence the count increments at twice the speed on the right to that on the left; this pulse rate doubling is consistent with the input voltage being doubled.

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Construction of the waveforms illustrated at 4 is aided by concepts associated with the Dirac delta function in that, by definition, all impulses of the same strength produce the same step when integrated. Then 4 is constructed using an intermediate step 6a hypothetical waveform not in the circuit but in which each integrated ideal delta function impulse is integrated to a step.

The effect of the finite duration of the actual pulse is constructed in 4 by drawing a line from the base of the impulse step at zero volts to intersect the decay line from 6 at the full duration of the pulse. In the circuit outside the loop, the summing interval is a predetermined fixed time, and at its expiry the count is stored, and the buffer and the counter are reset. The buffer then presents a sequence of digital values corresponding to quantizations of the analog signal levels during the summing intervals.

Using a summing interval is a way not necessarily the ideal way to quantize the asynchronous pulse stream to a code; it will have less quantization error if the interval start is synchronized to a pulse.

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Delta-sigma converters further constrain operation of the impulse generator such that the start of the impulse is delayed until the next occurrence of the appropriate clock-pulse boundary. A circuit diagram for a delta-sigma modulator implementation is shown in Figure 1b, with the associated waveforms in Figure 1c.The sampling rate of a signal should be higher than the Nyquist rate, to achieve better sampling. If this sampling interval in a Differential PCM DPCM is reduced considerably, the sample-to-sample amplitude difference is very small, as if the difference is 1-bit quantizationthen the step-size is very small i.

Sigma-Delta A/D Conversion

As the sampling interval is reduced, the signal correlation will be higher. The Delta Modulator comprises of a 1-bit quantizer and a delay circuit along with two summer circuits. Following is the block diagram of a delta modulator. The output quality of the waveform is moderate.

The delta demodulator comprises of a low pass filter, a summer, and a delay circuit. The predictor circuit is eliminated here and hence no assumed input is given to the demodulator. Low pass filter is used for many reasons, but the prominent one is noise elimination for out-of-band signals. The step-size error that may occur at the transmitter is called granular noisewhich is eliminated here.

If there is no noise present, then the modulator output equals the demodulator input. In digital modulation, we come across certain problems in determining the step-size, which influences the quality of the output wave. The larger step-size is needed in the steep slope of modulating signal and a smaller stepsize is needed where the message has a small slope.

As a result, the minute details get missed.

delta sigma modulation

Hence, it would be better if we can control the adjustment of step-size, according to our requirement in order to obtain the sampling in a desired fashion.

Delta Modulation Advertisements. Previous Page. Next Page. Previous Page Print Page.The objective of this exercise is to explore the concepts of Delta-Sigma modulation through a simple continuous time first order modulator.

The delta sigma modulator is the central part of delta sigma analog to digital converters which are also often referred to as over-sampling converters. In its simplest form, which features a single bit quantizer, it produces a bit stream. The digital average of this bit stream represents the input signal level. A simple continuous time first order delta sigma modulator block diagram is shown here:.

The difference between the analog input and the analog feedback DAC delta is integrated by the integrator sigma. The output of the integrator is quantized by comparing it to a threshold. The results of the comparison is sampled by the clocked latch and the digital output of the latch becomes the data output stream. A more in-depth explanation can be found in this mini-tutorial:.

The breadboard connections are as shown in figure 2.

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The digital pulse source output drives the clock input of the flip flop at pin 3. The waveform generator output is connected to resistor R 4 to provide the analog input test signals. Resistors R 1 and R 2 serve to split the supply voltage in half which provides a common mode bias point at the positive input of the opamp.

Referring back to the block diagram, the AD op-amp along with capacitor C 1 are the integrator function. The difference function takes place at the summing junction which is the negative input of the op-amp. The analog input voltage is converted into a current by resistor R 4.

The 1 bit digital to analog function DAC is performed by the Q output of the flip-flop and resistor R 3. Feedback resistor R 3 converts these two voltage levels into current which is also summed at the op-amp summing junction.

The difference in the current in R 3 and R 4 is integrated on capacitor C 1. The D input of the CMOS flip-flop will have a threshold voltage of approximately one half the power supply voltage and thus can serve as the comparator function.

The digital bit steam can be observed at the Qbar output of the flip-flop. The single pole RC low pass filter R 5 C 2 will serve as an analog reconstruction filter. The amplitude should be set to 5 V peak-to-peak with a 2. Waveform generator AWG1 should be set as a sine wave and to a frequency of 1 KHz with an offset of 0.The diagram inside the applet shows a basic first order sigma-delta modulator.

More sophisticated parts may have multiple modulators and integrators however these tend to obscure the underlying sigma-delta principle. This summing can be accomplished by means of a switched capacitor circuit which accumulates charge onto a capacitor summing node. An integrator then adds the output of this summing node to a value it has stored from the previous integration step. A comparator outputs a logic 1 if the integrator output is greater than or equal to zero volts and a logic 0 otherwise.

This feedback tries to keep the integrator output at zero by making the ones and zeros output of the comparator equal to the analog input.

The stream of 1's and 0's is subsequently digitally filtered not shown to produce a slower stream of multi-bit samples. The sigma-delta modulator loop typically runs at a much higher frequency than the final output rate of the digital filter. For example, a converter with a 2kHz output data rate may have a modulator loop frequency of over 2.

delta sigma modulation

Enter an ADC reference voltage in the lower input field. Enter the voltage to be converted in the V IN field. Click the Next Step button to move the tutorial forward a step.

At each step the diagram is updated to show the current output of each block. To see the outputs at the previous step of the tutorial, click the Previous Step button. To advance the tutorial complete loops of the modulator, click the Next Loops button.

The outputs from the comparator will be: 1, 0, 1, 1, 1, 0, 1, 1. This means 6 of the 8 outputs have been a 1; i. The allowed input range is With a 1.

delta sigma modulation

The digital filter does a much better job at detecting this trend then our simple count ones method. Instructions Related Information Instructions The diagram inside the applet shows a basic first order sigma-delta modulator. How to use this tool Enter an ADC reference voltage in the lower input field. Related Information.This circuit is original, at least to me. It seems like someone should have done this already, but I was unable to find anything similar online.

There are lots of based class-D amplifiers, but all the ones I found were using the control input and trying to PWM, rather than implement delta-sigma modulation. If you know of anything similar out there, please let me know via e-mail charles at steinkuehler dot net.

Videos with operating waveforms of the basic circuit and improved circuit are available on youtube. A delta-simga modulator is formed by quantizing the integral of the input signal minus the output.

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With a simple transform inverting the quantizer and changing the signs on the adder inputsthe above circuit turns into something we can build with a The delta-sigma modulator begins with a basic astable circuit using just two external components: a resistor and capacitor to set the timing.

In the astable circuit above, we already have two of the key delta-sigma components implemented. The resistor and capacitor from an integrator with positive feedback from the output, and the s internal comparators functions as an inverting quantizer. To provide for a signal input, we need a way to add the input term to the RC integrator network of the Assuming a voltage input, that means we need to connect a voltage to current converter between the input signal and the integrating capacitor, as shown in the following schematic.

Q12 forms a constant 1 mA current source, while Q11 is biased to sink 0 to 2 mA. At this point, the circuit is a completely functioning delta-sigma modulator.

The output can be filtered and used to efficiently drive a load class-D amplifier. Example waveforms of the operating circuit can be found on youtube. As an improvement, while the input voltage to current converter and the timing capacitor form a true integrator, the RC integrator for the output feedback is less than ideal.

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Adding an additional voltage to current converter, or implementing current-source feedback substantially improves the performance, particularly as the output level increases. Following is the basic delta-sigma modulator modified to include constant-current feedback from the output. Also shown is the output filter used for performance testing. Example waveforms of the improved circuit can be found on youtube.

Feedback from the 'net: In this design, a FET based current regulator is used for the feedback loop to improve the performance of the triangle wave generator. This information may have errors; It is not permissible to be read by anyone who has ever met a lawyer. Use is confined to Engineers with more than course hours of electronic engineering for theoretical studies. Email inform xtronics.