Noise shaping circuit and sigma-delta digital-to-analog converter

The present application provides a noise shaping circuit including a first modulation unit, configured to generate a first digital output signal according to a first digital input signal, the first modulation unit comprising a first quantizer; a first subtractor, coupled to an input terminal and an output terminal of the first quantizer, configured to generate a first quantization noise; and a second modulation unit, configured to generated a second digital output signal according to a second digital input signal, wherein the second digital input signal is related to the first quantization noise; wherein the noise shaping circuit generates an overall analog output signal according to the first digital output signal and the second digital output signal.

FIELD OF THE INVENTION

The present application relates to a noise shaping circuit and a sigma-delta digital-to-analog convertor (DAC), and more particularly, to a noise shaping circuit and a sigma-delta DAC capable of lowering noise energy.

BACKGROUND

Oversampling sigma-delta (ΣΔ) modulator is suitable for high resolution analog-to-digital convertor (ADC) or digital-to-analog convertor (DAC). For example, the sigma-delta DAC comprises an upsampling circuit, a filter, a quantizer, a digital-to-analog convertor and a low pass filter (LPF).

In order to increase the resolution of the sigma-delta DAC, it can be achieved by increasing the oversampling rate, increasing the order of filter, or even increasing the number of bits within the quantizer. Higher oversampling rate has a drawback of consuming more power. Higher filter order would cause energy of the out-of-band noise to be larger, and increase the cost of the backend analog low pass filter. In addition, even though more number of bits within the quantizer would reduce the out-of-band noise, however, under a condition of limited number of quantization bits, energy of the out-of-band noise is still high. Hence, the LPF with specific corner frequency is required to filter out the out-of-band noise.

The LPF is composed of an operational amplifier, resistor(s) and capacitor(s). Since noise is proportional to the resistance in the LPF, to achieve high signal-to-noise ratio (SNR), the resistance of the resistor is required to be small. However, to maintain the corner frequency of the LPF, the LPF needs the capacitor with large capacitance, which requires too large circuit area.

Therefore, it is necessary to improve the prior art.

SUMMARY

It is therefore a primary objective of the present application to provide a noise shaping circuit and a sigma-delta DAC capable of lowering noise energy, to improve over disadvantages of the prior art.

To solve the problem stated in the above, the present application provides a noise shaping circuit comprising a first modulation unit configured to generate a first digital output signal according to a first digital input signal, where the first modulation unit comprising a first filter, having a first transfer function; and a first quantizer coupled to the first filter; a first subtractor coupled to an input terminal and an output terminal of the first quantizer, configured to generate a first quantization noise; and a second modulation unit, configured to generated a second digital output signal according to a second digital input signal, wherein the second digital input signal is related to the first quantization noise, the second modulation unit comprises the second filter having a second transfer function; and the second quantizer coupled to the second filter; wherein the noise shaping circuit generates an overall analog output signal according to the first digital output signal and the second digital output signal.

Preferably, the noise shaping circuit comprises a third filter, having a third transfer function, coupled to the second modulation unit, configured to generate a filter result; wherein the noise shaping circuit generates the overall analog output signal according to the first digital output signal and the filter result.

Preferably, the noise shaping circuit comprises a fourth filter, having a fourth transfer function, coupled between the first subtractor and the second modulation unit, configured to generate the second digital input signal according to the first quantization noise.

Preferably, the fourth transfer function is related to the first transfer function and the third transfer function.

Preferably, the fourth transfer function is related to a reciprocal of the third transfer function.

Preferably, the third filter has a direct current (DC) gain, and the DC gain is less than 1.

Preferably, the third filter is a high pass filter.

Preferably, the third filter comprises an operational amplifier, comprising a first input terminal and an output terminal; a first resistor, coupled between the first input terminal and the output terminal of the operational amplifier, corresponding to a first resistance; a capacitor; and a second resistor, corresponding to a second resistance; wherein the capacitor and the second resistor are coupled between the first input terminal of the operational amplifier and the second modulation unit, the second resistance is the first resistance times a number, and the number is a reciprocal of the DC gain of the third filter.

Preferably, the noise shaping circuit comprises a first digital-to-analog convertor (DAC), coupled to the first modulation unit, configured to convert the first digital output signal as a first analog output signal; and a second DAC, coupled between the second modulation unit and the third filter, configured to convert the second digital output signal as a second analog output signal; wherein the third filter generates the filter result according to the second analog output signal; wherein the noise shaping circuit outputs the overall analog output signal as a summation of the first analog output signal and the filter result.

Preferably, a first filter order of the first filter is larger than or equal to a second filter order of the second filter.

The present application further provides a sigma-delta digital-to-analog convertor, comprising an upsampling circuit, configured to generate a first digital input signal; and a noise shaping circuit comprising a first modulation unit configured to generate a first digital output signal according to a first digital input signal, where the first modulation unit comprising a first filter, having a first transfer function; and a first quantizer coupled to the first filter; a first subtractor coupled to an input terminal and an output terminal of the first quantizer, configured to generate a first quantization noise; and a second modulation unit, configured to generated a second digital output signal according to a second digital input signal, wherein the second digital input signal is related to the first quantization noise, the second modulation unit comprises the second filter having a second transfer function; and the second quantizer coupled to the second filter; wherein the noise shaping circuit generates an overall analog output signal according to the first digital output signal and the second digital output signal.

The present application utilizes the two modulation units and the analog high pass filter to form the shaped noise spectrum with various slopes, and has advantage of being able to lower the noise spectrum, increase SNR and reduce circuit area.

These and other objectives of the present application will no doubt become obvious to those of ordinary skill in the art after reading the following detailed description of the preferred embodiment that is illustrated in the various figures and drawings.

DETAILED DESCRIPTION

In order to make the objects, technical solutions and advantages of the present application become more apparent, the following relies on the accompanying drawings and embodiments to describe the present application in further detail. It should be understood that the specific embodiments described herein are only for explaining the present application and are not intended to limit the present application.

Please refer toFIG. 1, which is a schematic diagram of a sigma-delta (ΣΔ) digital-to-analog convertor (DAC) according to an embodiment of the present application. The sigma-delta DAC10is an oversampling sigma-delta DAC. The sigma-delta DAC10, configured to convert a digital signal OD as an overall analog output signal OAA, comprises an upsampling circuit12and a noise shaping circuit14. The upsampling circuit12is configured to perform upsampling operation on the digital signal OD and generate a digital input signal ID1. The noise shaping circuit14comprises modulation units NS1and NS2, digital-to-analog convertors DAC1and DAC2, a subtractor SUB1and filters F3, F4. The modulation unit NS1, coupled to the upsampling circuit12, is configured to receive the digital input signal ID1and generate a digital output signal OD1. The modulation unit NS1comprises a filter F1and a quantizer Q1. The quantizer Q1is coupled to the filter F1, and the filter F1has a transfer function H1. The subtractor SUB1, coupled to an input terminal and an output terminal of the quantizer Q1, is configured to generate a quantization noise e1corresponding to the quantizer Q1. The modulation unit NS2, coupled to the subtractor SUB1, is configured to generate a digital output signal OD2according to a digital input signal ID2, where the digital input signal ID2is related to the quantization noise e1. In addition, the modulation unit NS2comprises a filter F2and a quantizer Q2. The quantizer Q2is coupled to the filter F2, and the filter F2has a transfer function H2. The noise shaping circuit14generates the overall analog output signal OAA according to the digital output signal OD1and the digital output signal OD2. In addition, a first filter order of the filter F1may be larger than or equal to a second filter order of the filter F2. In an embodiment, the filter F1may be a second order filter. The transfer function H1of the filter F1may be represented as H1(z)=z−1/(1−z−1)2. Preferably, the filter F2may be a first order filter. The transfer function H2of the filter F2may be represented as H2(z)=z−1/(1−z−1).

The filter F3is an analog filter with a direct current (DC) gain (i/G) and a transfer function Ha, where a value of the transfer function Ha corresponding to a DC frequency is 1. The filter F3, coupled to the modulation unit NS2, is configured to generate the filter result OA3. The noise shaping circuit14generates the overall analog output signal OAA according to the digital output signal OD1and the filter result OA3. The DC gain (1/G) of the filter F3is less than 1. In an embodiment, the filter F3is a high pass filter (HPF) with a corner frequency Fc. In other words, the filter F3would filter out signal of which frequency is less than the corner frequency Fc, and deliver signal of which frequency is larger than the corner frequency Fc.

The filter F4is a digital filter with an inverting DC gain (−G) and a transfer function Hc. The filter F4, coupled to the subtractor SUB1, is configured to perform filtering operation on the quantization noise e1, to generate the digital input signal ID2. The filtering operation the filter F4performs on the quantization noise e1is equivalent to multiply the quantization noise e1by the inverting gain (−G) and the transfer function Hc. Moreover, the transfer function Hc is related to the transfer function H1of the filter F1and the transfer function Ha of the filter F3. Preferably, the transfer function Hc is related to a reciprocal of the transfer function Ha. RegardingFIG. 1, the transfer functions Hc, H1and Ha have a relationship of 1/(1+H1)=Hc*Ha in between. Specifically, the transfer function Hc may be represented as Hc(z)=1/(1+H1(z))/Ha(s)|s→z, where Hc(z) represents a function of the transfer function Hc in z-Domain, H1(z) represents a function of the transfer function H1in z-Domain, Ha(s) represents a function of the transfer function Ha in s-Domain, and Ha(s)|s→zrepresents a function of the transfer function Ha in z-Domain, i.e., Ha(s)|s→zis the function converting Ha(s) from s-domain to z-domain. For illustrative purpose, the transfer function Hc may be simply represented as Hc=1/(1+H1)/Ha=1/[(1+H1)·Ha].

In addition, the digital-to-analog convertors DAC1and DAC2are coupled to the modulation units NS1and NS2, configured to convert the digital output signals OD1and OD2as analog output signals OA1and OA2, respectively. The filter F3, coupled to the digital-to-analog convertor DAC2, is configured to perform filtering operation on the analog output signal OA2. The filtering operation the filter F3performs on the analog output signal OA2is equivalent to multiply the analog output signal OA2by the DC gain (1/G) and the transfer function Ha, to generate the filter result OA3. In the current embodiment, the noise shaping circuit14outputs the overall analog output signal OAA as a summation of the analog output signal OA1and the filter result OA3.

In addition, please refer toFIG. 2andFIG. 3.FIG. 2is a schematic diagram of equivalent circuit model of another noise shaping circuit24according to an embodiment of the present application.FIG. 3is a schematic diagram of shaped noise spectrum. The noise shaping circuit24comprises modulation units NS1″ and NS2″, and filters F3″ and F4″. InFIG. 2, s represents the digital input signal ID1, e1represents the quantization noise brought by the quantizer Q1, e2represents the quantization noise brought by the quantizer Q2. InFIG. 3, a dashed line represents a noise spectrum after a first order shaping, a dotted line represents a noise spectrum after a second order shaping, a solid line represents a noise spectrum of the noise shaped by the noise shaping circuit24. For brevity, effect caused by the digital-to-analog convertor DAC1and DAC2on the noise shaping circuit14is ignored in the following description.

The modulation unit NS1″ performs noise shaping on the quantization noise e1after receiving the digital input signal ID1(corresponding to the signal s). The signal outputted by the modulation unit NS1″ may be represented as s+e1*(1−H1). In addition, the filter F4″ performs filtering operation on the quantization noise e1. Hence, the signal outputted by the filter F4″ may be represented as G·Hc·e1. The modulation unit NS2″ receives the output signal G·Hc·e1outputted by the filter F4″ and performs noise shaping on the quantization noise e2. The signal outputted by the modulation unit NS2″ may be represented as −G·Hc·e1+e2·(1−H2). The filter F3″ performs filtering operation on the signal outputted by the modulation unit NS2″. Since the transfer function Hc of the filter F4″ and the transfer function Ha of the filter F3″ have the relationship of Hc=(1−H1)/Ha and the DC gain of the filter F3″ is (1/G), the components within the output signal outputted by the modulation unit NS1″ related to the quantization noise e1can be cancelled by the components within the output signal outputted by the modulation unit NS2″ related to the quantization noise e1. Therefore, the signal outputted by the noise shaping circuit24(corresponding to the overall analog output signal OAA) may be represented as s+e1·(1−H1)−e1·Hc*Ha+(1/G)e2·Ha·(1−H2)=s+(1/G)e2·Ha·(1−H2).

Notably, within the signal outputted by the noise shaping circuit24, the signal component related to the quantization noise is (1/G)e2·Ha·H2, where the filter F2″ may be a first order filter. The transfer function H2may be represented as H2(z)=z−1. In an embodiment, the filter F3″ may be a first order high pass filter within the corner frequency Fc. In other words, when frequency is less than the corner frequency Fc, the transfer function Ha is approximately in a first order attenuation; when frequency is larger than the corner frequency Fc, the transfer function Ha is 1. In such a situation, when frequency is less than the corner frequency Fc, the filter F2is a first order filter and the transfer function Ha would apply a first order attenuation on the signal e2·H2. Thus, the noise shaping circuit24would perform a second order noise shaping on the quantization noise. On the other hand, when the frequency is larger than the corner frequency Fc, the transfer function Ha is 1 and the filter F2is still a first order filter. Thus, the noise shaping circuit24would perform a first order noise shaping on the quantization noise. In other words, the noise shaping circuit24utilizes the inverting DC gain (−G) of the filter F4to replace the quantization noise e1brought by the modulation unit NS1″(i.e., e1·(1−H1)) with the quantization noise e2brought by the modulation unit NS2″ (i.e., (1/G)e2·Ha·(1−H2)). Since the quantization noise e2is processed by the filters F2′ and F3′ via the transfer functions H2and Ha, the shaped noise spectrum would be the spectrum illustrated as the solid line inFIG. 3.

In comparison, please refer toFIG. 4, which is a schematic diagram of an oversampling sigma-delta DAC40in the art. The oversampling sigma-delta DAC40comprises the noise shaping circuit44, and the noise shaping circuit44comprises a filter F. When the filter F is a second order filter, the noise spectrum shaped by the noise shaping circuit44is the dotted line inFIG. 3and a slope of the noise spectrum is larger. Advantage of the filter F being the second order filter is that the noise energy is low within a signal band SB, but disadvantage thereof is that the noise energy is too large at high frequency. When the filter F is a first order filter, the noise spectrum shaped by the noise shaping circuit44is the dashed line inFIG. 3and a slope of the noise spectrum is smaller. Advantage of the filter F being the first order filter is that the noise energy is lower at high frequency, but disadvantage thereof is that the noise energy is larger within the signal band SB.

Notably, the noise spectrum shaped by the noise shaping circuit24has the property of the second order noise shaping within the signal band SB (i.e., lower noise energy within the signal band SB), and also has the property of the first order noise shaping outside the signal band SB or even at high frequency, (i.e., lower noise energy at high frequency). In other words, the noise shaping circuit24may own advantages of both the first order noise shaping and the second order noise shaping, which means that the noise spectrum shaped by the noise shaping circuit24has low noise energy both within the signal band SB and at high frequency. Furthermore, the filter F3has the DC gain (1/G) and the DC gain (1/G) is less than 1. After the noise spectrum shaped by the noise shaping circuit24(corresponding to the solid line inFIG. 3) is further shifted downward by a factor G, compared to the noise spectrum by the first order shaping (corresponding to the dashed line inFIG. 3), where the noise energy is further reduced.

In addition, the noise shaping circuit14inFIG. 1is not limited to be realized by certain circuit structure. For example, please refer toFIG. 5, which is a schematic diagram of a sigma-delta DAC50according to an embodiment of the present application. The sigma-delta DAC50comprises a noise shaping circuit54, and the noise shaping circuit54comprises modulation units NS1′ and NS2′, and filters F3′ and F4′. The modulation units NS1′ and NS2′ and the filters F3′ and F4′ are configured to realize the modulation units NS1and NS2and the filters F3and F4of the noise shaping circuit14inFIG. 1, respectively. Operational principle of the noise shaping circuit54is the same as which of the noise shaping circuit14, which is not narrated herein for brevity. Notably, the filter F3′ is an analog high pass first order filter, which comprises the operational amplifier OP, a capacitor C, a resistor R and a resistor G*R, where a resistance of the resistor G*R is G times a resistance of the resistor R. The resistor R is coupled between a negative input terminal (denoted by “−”) and an output terminal of the operational amplifier OP. The resistor R and the resistor G*R are coupled between the negative input terminal of the operational amplifier OP and the output terminal of the digital-to-analog convertor DAC2. In addition, since the resistance of the resistor G*R is G times the resistance of the resistor R, the DC gain of the filter F3′ is (1/G), such that the noise spectrum shaped by the noise shaping circuit54is able to be shifted downward by the factor G. Furthermore, the corner frequency Fc of the filter F3′ may be represented as 1/(2πGRC). When G is sufficiently large, the capacitance of the capacitor C is not required to be large to maintain the corner frequency Fc to be a specific value. In other words, the noise shaping circuit54does not need the capacitor C with large capacitance, which means that the circuit area is reduced.

As can be seen, the noise shaping circuit24utilizes the subtractor to capture the quantization noise e1corresponding to the quantizer Q1; utilizes the filters F3″ and F4″ to recover the signal component related to the quantization noise e1within the signal outputted by the modulation unit NS2″ as e1·(1−H1), so as to cancel the signal component related to the quantization noise e1within the signal outputted by the modulation unit NS1″; utilizes the filters F2″ and F3″ to shape the quantization noise e2to be the spectrum illustrated as the solid line inFIG. 3; and utilizes the resistor G*R to lower the noise spectrum, increase signal-to-noise ratio (SNR), and reduce circuit area.

Notably, the embodiments stated in the above are utilized for illustrating the concept of the present application. Those skilled in the art may make modifications and alterations accordingly, and not limited herein. For example, the filter F1is not limited to be a second order filter. The filter F1may be a filter with even higher order, which is also within the scope of the present application.

In summary, the present application utilizes the two modulation units and the analog high pass filter to form the shaped noise spectrum with various slopes, which incorporates properties of both low order noise shaped spectrum and high order noise shaped spectrum. The present application has advantage of being able to lower the noise spectrum, increase SNR and reduce circuit area.

The foregoing is only embodiments of the present application, which is not intended to limit the present application. Any modification following the spirit and principle of the present application, equivalent substitutions, improvements should be included within the scope of the present invention.