PDM-based D/A conversion technology

1 Introduction

In digital signal processing, it is often necessary to convert a multi-digit signal into a digital signal. For example, in the communication field, if a receiver receives an encoded digital voice signal, it must convert it into a simulated signal to restore the original analog voice signal. The encoded voice signal is usually a multi-bit stream. Therefore, how to convert multiple bits into analog voice signals becomes the key to ensuring communication quality. For example, in some control circuits, the control signal is a multi-digit digital signal generated after computation, and these digital signals must be converted to analog signals to control the circuit. Therefore, how to convert a multi-digit signal into a simulated signal that meets the actual requirements has become the most concern of the control circuit designers.

In traditional circuit design, in the face of the above problems, a D/A converter consisting of multiple separated electronic components is usually used, sometimes we call it a static D/A converter. However, due to the composition of the static D/A converter, it determines that it must occupy a certain amount of space and consume a certain amount of power in the system. Therefore, in system solutions that require convenient portability, the static D/A converter has to be replaced with [1].

So people choose the so-called "Digital basis" D/A converter. There are two methods for digital D/A conversion: PWM (P Ulse Width Modulation) Pulse Width Modulation and PDM (pulse density modulation) pulse density modulation. This digital D/A converter occupies less physical space and consumes less power. Therefore, it is suitable for systems with strict requirements on system hardware size and power consumption [1].

As early as 1940s, PWM began to be applied on the phone. Due to limitations of PWM, a PDM modulation method was proposed 20 years later. However, since the current application market was not yet large enough, this modulation method has not been widely concerned and applied. In recent years, due to the wide application of digital technology in various fields, the rapid development of digital products has attracted more and more attention in digital signal processing. Therefore, PDM modulation technology has been paid more attention and applied in different fields.

2. Basic Introduction to PDM

PDM is a modulation method that provides analog signals in the digital field. In the PDM signal, the logical "1" indicates a single pulse, and the logical "0" indicates no pulse. Generally, the logical "1" and logical "0" are not consecutive, and the logical "1" is evenly distributed in each modulation signal cycle. One pulse does not represent the amplitude, but the density of a series of pulses corresponds to the amplitude of the analog signal. A pdm signal completely composed of "1" corresponds to a positive voltage, while a PDM signal completely composed of "0" corresponds to a negative voltage; the signal that is composed of alternating values of 1 and 0 corresponds to the voltage of the 0 amplitude.

3. Implementation of PDM

The logical Diagram 1 of PDM modulation technology is shown in. One frequency-division counter is used to implement the clock signal that meets the actual application requirements. The pulse cycle is △t. Then send the clock signal? N-bit counters, implementing 0, 1 ,..., 2n-1 count. In the single pulse period △t of the count, the logical values of each bit in the count result are processed through a series of logical operations to realize the n-bit comparison benchmark pulse signals, which are bit0, bit1, bit2, ..., Bit (n
-1 ). It is worth noting that in every delta T, there is only one bit with the logical "1" and the other bit with the logical "0 ". At the same time, compare the n-bit bus data output by the register with the bit0, bit1, bit2 ,..., Bit (N-1) for bitwise AND operation, and then the results of each bit or, then get the delta T tuning results. In this way, the modulation result is obtained after the entire modulation cycle ends.

For N-bit digital signals, the modulation period t is 2n · △t. For an 8-bit digital signal to be tuned, the modulation result of △t in each pulse cycle is:


For example, the 8-bit hexadecimal digital signal "1ah" is modulated. Use an 8-bit counter to generate a comparison Pulse Signal shown in 2. Obviously, bit0 ~ In bit7, only one bit has a pulse.

The hexadecimal number "1ah" corresponds to the binary number "00011010", where bit4, bit3, and bit1 are "1", and others are "0". After a bit-by-bit logical operation, that is:

After a modulation period, the modulation signal shown in 3 is obtained. In this way, the 8-bit digital signal is converted into a one-bit pulse signal.

4 Analysis and Comparison of PDM and PWM

After the digital signal is modulated by PDM, digital-analog conversion can be realized through a simple low-pass filter. To facilitate the comparison, in the simulation, set the length of the digital signal to be adjusted to 2 characters, respectively, "1ah, a1h ". The pulse period delta T is 1 MS, and the time of one modulation period is 256 Ms.

The selection of different R and C values in the RC Filter Circuit has a great impact on the accuracy of the modulation result and the duration of the rising and falling edges.

(1) rc = 50 · △t?

Figure 4 shows the analog signal output by RC filtering after the 8-bit characters "1ah, a1h" are modulated by PDM. Its Communication ripple is small, but the signal response speed is slow, that is, the rising edge of the signal changes is relatively relaxed.

As shown in figure 5, two 8-bit characters, "1ah, a1h", are modulated by PWM to simulate signals output after RC filtering. Obviously, the AC ripple composition is much larger than the analog signal after PDM modulation.

(2) rc = 10 · △t

Figure 6 shows that when rc = 10 · △t, two 8-bit characters, "1ah, a1h", are modulated by PDM and the analog signal output after RC filtering, the amplitude of the AC ripple is about 20% of the DC composition, and the response time is about 7.5% of the modulation cycle.

The above simulation results show that, compared with the PWM modulation signal, after the PDM modulation signal passes through the low-pass filter, the AC composition in the simulation signal is obviously weakened, that is, the noise is relatively small. For PDM modulation, the larger the RC value in the RC filtering network, the less the AC component in the analog signal, and the slower the response speed.

Therefore, the rational selection of R and C values enables the size and response speed of the AC components to meet the requirements of practical applications, which is the key to system design.

5. Application of PDM

In recent years, PDM has been widely used in various fields of digital systems. In the communication field, Speech Signal Restoration in many communication tools uses PDM technology [2].

Almost all CDMA mobile phones use the proprietary PDM technology. In the field of control, many control units, such as power management, also use PDM technology [2]. In the audio electronics field, PDM technology has also been widely used, such as digital microphones in many consumer electronic products [3].

Of course, PDM technology also has its own limitations. For example, when the number of digits to be modulated increases, the modulation cycle increases accordingly and the response speed of the filter decreases accordingly. However, in the modulation method used for D/A conversion, PDM is an ideal method.