The relationship between digital and analog signals in electronic design is inextricably linked. Although on the surface digital and analog signals may seem completely different, a deeper analysis reveals that digital signals are essentially a manifestation of analog signals. We can understand this more clearly through means such as spectrum analysis. In addition, the PCB (printed circuit board) plays a crucial role in signal transmission and can be seen as a filter. In this article, we will analyze the characteristics of digital signals and their relationship to analog signals from the perspective of signal integrity.
Spectrum analysis of digital signals
A digital signal is typically represented by a series of discrete voltage levels, such as 0 and 1. However, from a spectral point of view, a digital signal can be seen as a complex waveform with a rich harmonic component. Each square wave signal can be decomposed into a superposition of an infinite number of sine waves, known as a Fourier series representation. For example, a square wave signal with frequency ff has a spectrum that contains the fundamental frequency ff and all odd harmonic components 3f, 5f, and 7f,......。
The relationship between digital and analog signals
From the spectrum analysis, we can see that a digital signal is actually composed of a series of sine waves of different frequencies and amplitudes. This means that a digital signal is also an analog signal in nature. This realization is critical to understanding and designing high-speed digital circuits, where the high-frequency component of the signal can significantly affect circuit performance and signal integrity.
The PCB acts as a filter
PCBs play a vital role in digital signal transmission, with transmission line characteristics, impedance matching, and electromagnetic interference control all directly impacting signal integrity. Think of the PCB as a filter because it selectively attenuates the signal passing through it. Specifically, factors such as the material of the PCB, the width and length of the traces, and the structure of the wiring layer can all affect the transmission characteristics of the signal. For high-speed signals, transmission line effects are more pronounced and therefore need to be specifically designed to avoid signal reflections, crosstalk, and attenuation.
A transmission line is a device used to transmit energy and signals, and due to its wide range of applications, it has become a very interesting object of study. In long-distance transmission cables, long-distance communication lines, and high-frequency circuits, it is important to calculate and control the efficiency and stability of signal transmission. The parameters of the transmission line are often distributed over the entire length, so a uniform transmission line model is required for simplification and analysis.
Uniform transmission line model
The uniform transmission line model is an important and simple model in the theory of circuits and electromagnetic fields. A typical uniform transmission line consists of two parallel metal conductors placed in a homogeneous medium, and common forms include parallel double pairs, coaxial wires, and parallel plates. In practice, there is no ideal uniform transmission line, because the unloaded bracket and the voltage gradient of the wire itself will make the transmission line uneven. To simplify the problem, these unimportant factors need to be ignored.
Assuming that the transmission line is homogeneous, i.e., the distance between the two conductors, the cross-section shape, and the electrical properties of the medium remain constant over a long length, the resistance RR and inductance LL per unit length are constant. Similarly, the line capacitance CC and conductance GG per unit length are also constant. At the very end of the transmission line is the load, which is denoted as Z0Z_0. Select a very small transmission line with a length of Δx\Delta x and analyze it.
For a small paragraph Δx\Delta x, it can be thought of as a lumped parameter system, i.e.:
RΔx,LΔx,GΔx,CΔxR \Delta x, L \Delta x, G \Delta x, C \Delta x
When Δx\Delta x approaches zero, the model approximates the actual distribution parameter system.
Important parameters and explanations
- Resistance RR: The resistance of a conductor, the greater the resistance per unit length, the more pronounced the attenuation of the signal.
- Inductance LL: The inductance per unit length affects the phase, speed, and transmission characteristics of the signal.
- Conductance GG: The conductance of the medium, the greater the conductance per unit length, the more energy loss of the signal.
- Capacitance CC: The capacitance between conductors, the larger the capacitance per unit length, the smaller the characteristic impedance of the transmission line.
A uniform transmission line can be equivalent to a combination of lumped elements RLGC in a segment. Because R and G are negligible, they can eventually be simplified to a segment LC circuit.
In the case of high frequencies, the influence of the wire resistance RRR and the dielectric conductance GGG is less than that of the inductor LLL and the capacitance CCC, so the transmission line model can be simplified and the RRR and GGG can be ignored to obtain an ideal LC circuit model.
Low-pass filter
The frequency response of an ideal transmission line is similar to that of a low-pass filter. The transmission line has a higher attenuation of the high-frequency components, which is due to the combination of inductance and capacitance of the transmission line. For example, in the case of high frequencies, the transmission line will limit the transmission of the high-frequency signal due to the high impedance of the inductor to the high-frequency signal and the low impedance of the capacitor to the high-frequency signal, thus exhibiting the characteristics of a low-pass filter.
Frequency response analysis
Through the frequency response analysis, it can be seen that the ideal transmission line has selective transmission characteristics for signals of different frequencies. For example, for a transmission line with a length of lll, the characteristic impedance is:
The cut-off frequency of the transmission line fcf_cfc is determined by the inductance and capacitance of the transmission line:
Signals below the cut-off frequency can be transmitted efficiently, while signals above the cut-off frequency are significantly attenuated.
A uniform transmission line can be equivalent to a lumped LC circuit in a high-frequency circuit, and the transmission line behaves like a low-pass filter after ignoring resistance and conductance. This simplified model makes it easier for engineers to analyze and design the frequency response characteristics of transmission lines, ensuring signal integrity and system performance. This equivalent model is important for understanding and optimizing the design of PCB traces.
So for PCB routing, the high-frequency component is suppressed, the square wave is not so "square", and the rising edge is not so vertical.
Signal integrity is an important step in ensuring that digital signals are transmitted without distortion and excessive noise. Common signal integrity issues include reflections, crosstalk, impedance mismatch, ground bounce, and power supply noise. The root cause of these problems can often be traced back to the spectral characteristics of the signal and the transmission characteristics of the PCB. For example, high-speed signals have a higher frequency component and are more susceptible to the adverse effects of PCB traces.
Through spectrum analysis, we can clearly see that a digital signal is actually a special form of analog signal, and its spectrum contains a rich harmonic component. As a carrier of signal transmission, the characteristics of the PCB directly affect the integrity of the signal and must be designed and optimized as a filter. Understanding the intrinsic relationship between digital and analog signals helps us better analyze and solve signal integrity issues in electronic design, thereby improving the reliability and performance of circuits.
overview
Hardware is not wired
I do hardware, several stages of advancement
signal
Why do you need to amplify analog signals?
The basic concept of filters
First-order RC low-pass filter
Why do I need anti-aliasing filtering?
High-speed ADC foundation
—Recommended Books—
【Recommended Book】"Fundamentals of Circuit Design Engineering Calculation" Wu Yeqing
【Recommended Book】100,000 Whys of Hardware (Development Process)
【Recommended Book】100,000 Hardware Whys (Passive Components)
【Recommended Book】"High-speed Circuit Design Practice" Wang Jianyu
【Recommended Book】ADS Signal Integrity Simulation and Actual Combat, Second Edition, Jiang Xiuguo