Create Seamless Waveforms with Raspberry Pi Pico PIO

Table of Contents

1. Introduction
2. Understanding the Programmable Input Output Features of the RP2040
3. The Need for Minimizing Frequency Jitter in the AWG
4. The Theory Behind the Arbitrary Wave Generator
   • 4.1 Wave Table and Memory Locations
   • 4.2 The Role of the Programmable Input Output (PIO)
   • 4.3 Digital to Analog Conversion
   • 4.4 Amplification with Operational Amplifiers
5. Previous Attempts to Minimize Frequency Jitter in the AWG
6. Expanding the Wave Table for Improved Symmetry
   • 6.1 The Nyquist Sampling Theorem
   • 6.2 Choosing the Number of Cycles per Wave Table
   • 6.3 Increasing Wave Table Buffer Size
7. Comparing Jitter-Free Prime Frequencies
   • 7.1 Jitter Reduction with Integer Divisors
   • 7.2 Frequency RMS Measurement
8. Testing the New Method with Different Waveforms
   • 8.1 Sine Wave Jitter Comparison
   • 8.2 Square Wave Jitter Comparison
   • 8.3 Triangle Wave Jitter Comparison
9. Combining Methods for Low and High Frequencies
   • 9.1 The Revised AWG Program
   • 9.2 Generating Very Low Frequencies
10. Conclusion
11. Using the Raspberry Pi Pico W for Audio Synthesis
12. Wrap Up and Future Possibilities

Introduction

Welcome to another day in life with David! In this article, we will continue our exploration of the programmable input output (PIO) features of the RP2040 microcontroller. Specifically, we will focus on the arbitrary wave generator (AWG) and the challenge of minimizing frequency jitter in its output. We will delve into the theory behind the AWG, discuss previous attempts at mitigating frequency jitter, and explore new methods for achieving more stable waveforms. Join me as we dive into the world of AWG and unlock the secrets to smoother wave generation.

Understanding the Programmable Input Output Features of the RP2040

Before we delve into the intricacies of the AWG, let's take a moment to understand the programmable input output features of the RP2040. The RP2040 is a powerful microcontroller developed by Raspberry Pi, capable of performing a wide range of tasks. One of its standout features is the ability to generate arbitrary waveforms through the AWG. This feature allows us to create custom waveforms for various applications such as signal testing, audio synthesis, and more. However, as we will soon discover, generating stable and jitter-free waveforms can be quite challenging.

The Need for Minimizing Frequency Jitter in the AWG

In our previous experiments with the AWG, we successfully increased the frequency range of an arbitrary waveform generator by incorporating a high-speed operational amplifier and revising the software. However, we faced a recurring issue with frequency jitter that rendered the AWG unusable for real-world testing applications. This frequency jitter, although expected when using fractional divisors to generate the state machine clock, posed a significant challenge in achieving stable waveforms, particularly for square and triangle waves. In this article, we aim to address this issue and explore methods to minimize frequency jitter in the AWG.

The Theory Behind the Arbitrary Wave Generator

The arbitrary wave generator operates on the principle of storing waveform data in a contiguous set of memory locations known as a wave table. This wave table consists of values that represent the desired waveform. The information stored in the wave table is repeatedly outputted using direct memory access to the programmable input output (PIO). The PIO, which runs at the state machine clock frequency, outputs 8-bit parallel information to a digital-to-analog converter (DAC). The resulting analog signal is then amplified by a high-speed operational amplifier to achieve the desired waveform. However, to ensure waveform continuity, the starting and ending bytes of the wave table must match.

4.1 Wave Table and Memory Locations

The wave table plays a crucial role in the generation of arbitrary waveforms. A wave table is essentially a contiguous block of memory locations that holds the values representing the waveform. The length of the wave table determines the precision and resolution of the generated waveform. In our initial setup, we used a wave table length of 256 bytes, which limited the number of cycles and the overall symmetry of the waveform. However, by expanding the wave table size, we can achieve higher resolution and more symmetric waveforms.

4.2 The Role of the Programmable Input Output (PIO)

The programmable input output (PIO) is responsible for orchestrating the generation of waveforms in the RP2040. It operates at the state machine clock frequency and handles the output of waveform data from the wave table. Utilizing direct memory access, the PIO transfers the waveform data to a digital-to-analog converter (DAC) for conversion into an analog signal. This digital-to-analog conversion process is fundamental in producing the desired waveform. By modifying the state machine clock frequency, we can control the frequency of the generated wave.

4.3 Digital to Analog Conversion

After the waveform data is retrieved from the wave table by the PIO, it undergoes digital-to-analog conversion. This conversion process transforms the digital representation of the waveform into an analog signal. The digital waveform, consisting of discrete values, is converted into a continuous analog signal that accurately represents the desired waveform shape. This analog signal feeds into an operational amplifier for further amplification and shaping.

4.4 Amplification with Operational Amplifiers

To ensure that the generated waveform reaches the desired level of amplitude and fidelity, we utilize operational amplifiers for amplification. These high-speed operational amplifiers take in the low-level analog signal and amplify it to a level suitable for the intended application. By carefully selecting and configuring the operational amplifiers, we can shape the waveform, increase its amplitude, and minimize distortion.

With a solid understanding of the theory behind the AWG, we can now explore the challenges we faced in minimizing frequency jitter and creating smoother waveforms. Stay tuned as we dive deeper into the methods and techniques used to achieve this goal.