Reflection Rule Calculator for Impedance Matching

Whenever a signal is sent digitally from one point to another, it changes the state of a signal line. The change in state of the signal can be described as an electromagnetic wave as it moves through the circuit. Reflection in the signal occurs when an electromagnetic wave encounters a boundary from one medium to the next. When the wave meets the boundary, part of the energy is transmitted as a signal and part of it is reflected. The process will continue indefinitely until the energy is absorbed by the circuit or dissipated into the environment.

For electrical engineers, the medium where this boundary occurs is usually described in terms of its electrical impedance; that is, the boundary is where impedance changes.

Reflections in a PCB design occur when an electrical signal encounters an impedance mismatch as it travels along a trace. This mismatch causes a portion of the signal to be reflected back towards the source. Reflections can lead to signal integrity issues, such as distortion, noise, and data errors, particularly in high-speed digital or RF circuits.

How Reflection Noise is a Problem?

Due to reflections in the signal line, extra energy is accumulated in the path which causes the noise problems in the signal. The reflection noise pushes the signal towards unpredictable value and changes the overall shape of a deterministic signal into a random signal. The job of the engineer is to minimize the amount of reflected signal and maximize the amount of transmitted signal through impedance matching. So, the additional energy will be dissipated before it accumulates and drowns out a signal with noise.

If the energy of the reflected pulse does not dissipate before the next pulse is generated, the energy will accumulate and add in a phenomenon called superposition. After reflection if the phase and amplitude of the wave aligns with the original signal the formation of standing waves will be there. If standing waves are formed in the transmission line the enormous noise is introduced into the signal path. Fortunately, signals attenuate as they pass through resistive elements. So a simple series resistor may help to reduce this parasitic effect. We will discuss some more methods to reduce the noise later in this article.

Analysis of Noise in Digital Signals:

Fourier’s theorem shows that a digital wave can be represented in the form of decomposed components of harmonically related sine and/or cosine waves. If you have a sufficiently small rise/fall time, a single pulse can hold in it dozens of small-amplitude waves.

In the image below, you can see an undamped digital signal switching logic states from low to high. For signals of practical interest, we can decompose the waveform into a series of sine waves. As the above figures show, a real digital signal has a large bandwidth and any portion of that energy might create a resonance in your circuit. This is in contrast to RF signals that have very narrow bandwidth with easy to calculate resonances.

Impedance of a Circuit:

In circuits with resistors, inductors, and capacitors, the total equivalent resistance that hinders the flow of current in the circuit is called impedance. Impedance is composed of resistive and reactive elements. Resistors dissipate a circuit’s energy as heat. The recoverable energy in a circuit exists in the electromagnetic fields that permeate and surround conductors, inductors, and capacitors.

Impedance is commonly represented by the symbol "Z" and is a complex number, with the real part known as resistance and the imaginary part known as reactance. Capacitive reactance refers to the impedance offered by capacitors to alternating current in a circuit, while inductive reactance refers to the impedance offered by inductors to alternating current. The combined impedance resulting from capacitive and inductive reactance to alternating current is referred to as impedance. The unit of impedance is ohms.

What is Impedance Control in PCB Design?

High speed circuits work on frequencies up to some GHz. Due to which high frequency circuits are more prone to noise and need special design procedures. The circuit board itself may vary in process parameters, leading to changes in impedance and causing signal distortion. Therefore, for conductors on high-speed circuit boards, their impedance values need to be controlled within a specific range, a practice known as "impedance control." PCB designers typically need to implement impedance control for PCBs used in high-speed digital applications, high-speed signal processing, and high-quality analog video (e.g., DDR, USB, SSD, Gigabit Ethernet).

The behaviour of circuits at high frequencies change due to parasitic effects like fringe capacitance and inductance. PCB signal traces also behave like transmission lines, and every point along the signal trace has impedance. As a result, the original signal becomes distorted, and what was intended to be transmitted from the transmitting end may change by the time it reaches the receiving end. Therefore, to achieve distortion-free signal transmission, PCB signal traces must maintain consistent impedance. This is the first step in improving signal integrity on PCB trace routing.

How to do Calculation of Impedance in PCB design:

Impedance of transmission lines is determined when the layer stackup for your design is created. Having the ability to change the following board layer attributes gives you control over your impedance, losses, and propagation delay during routing. When designing a PCB stackup, the designer needs to set the layer arrangement and layer thicknesses, and they need to select materials for their PCB. Once these decisions are made, a designer needs to determine the PCB trace width required to hit their required PCB transmission line impedance.

PCB transmission line calculators are a dime a dozen, giving you the tools you need to calculate lossless impedance, lossless propagation delay, or simple things like DC resistance. These quantities are nice to know, but they don't tell you the whole story about your design. Online calculators are also known to give incorrect results when used for impedance calculations, especially because they cannot consider fundamental phenomena like dispersion and roughness in transmission lines.

Online calculators will generally use Wadell's equations to determine the transmission line impedance numerically. Simpler calculators will use the less-accurate IPC-2141 equations. A PCB transmission line calculator you'll find online or in many design applications can't be used to get accurate impedance values because they do not include a consideration for loss tangent or dispersion in these calculations. Therefore, a more accurate utility is needed for these tasks.

Factors Determining Transmission Line Impedance:

Factors that Influence Impedance is determined by several factors:

• Real part of the dielectric constant: Dielectric thickness is directly proportional to impedance. The thicker the dielectric, the higher the impedance.

• Loss tangent and dispersion: Loss tangent in PCB design measures the dielectric material's energy loss as heat when a signal passes through it. It impacts signal integrity, especially at high frequencies, causing signal attenuation. Lower loss tangent materials are preferred for high-speed and RF designs to reduce signal degradation.

• Distance between the trace and the nearby reference plane: Distance between two traces are inversely proportional to the impedance. Proper spacing is critical for maintaining controlled impedance, ensuring signal integrity in high-speed and RF circuits.

• Copper trace thickness and roughness: Copper foil thickness is inversely proportional to impedance. The thicker the copper, the lower the impedance. Copper thickness can be controlled through pattern electroplating or selecting base material copper foil with the appropriate thickness.

• Trace width: Trace width is inversely proportional to impedance. Thinner trace widths come with higher impedance, while wider trace widths come with lower impedance. Controlling trace width within a tolerance of +/- 10% is necessary for better impedance control. To ensure trace width accuracy, engineering compensation is performed on the photomasks based on etch undercut, lithographic errors, and pattern transfer errors.

How to Reduce Reflection Noise:

There are several methods you can use to manage reflection noise in your design. Here's an overview of some of the techniques at your disposal.

1. Calculate the impedance of your traces

Maintain Constant Impedance after the trace crosses an element, via or component pad. In order to maintain constant impedance, you'll need to be able to calculate the impedance of your traces. Your PCB program should allow you to do this, but there are also online tools available. Once you determine what your trace and space widths are, maintain them along your routes.

2. Consistency across traces

To maintain constant impedance in your differential pairs or single-ended traces, you must maintain constant trace-width, constant spacing, and constant separation from all other conductors. If you route over your impedance-controlled pairs with a random trace, you will change the impedance and create a point of reflection.

3. Reduce Reflection Points

You can also consider how to reduce the occurrence of reflection points in the first place.

4. Watch your vias at the edge of the board

Vias can be a problem for high-speed circuit designers. If the via extends beyond the signal traces to unused layers, the impedance of the circuit suddenly changes. At the transition at the edge of a board, there is an impedance mismatch as the traces leave the via (~50-150 ohms) and enter air (~377 ohms). This creates a reflection point at that location that can severely degrade a signal.

5. Back-drill your vias

The solution is to have your PCB manufacturer “back-drill” your vias to remove the via from the board on the unused outer layers. Back-drilled vias significantly improve logic transitions.

Mitigate Existing Reflection Noise:

Another important technique is to use damping resistors in series near all driving signal sources with fast rise/fall times. This is sometimes referred to as a snubbing resistor. Any signal reflection that occurs will be quickly attenuated by each pass through the resistor. These are typically <100Ω resistors placed close to the driving signal source (e.g., clock source, GPIO, etc…). The general idea is to create a damped circuit—where the signal rises to the appropriate logic level once without excessive overshoot and ringing.

Calculation of Reflection Rules in a Design:

There are mainly 3 parameters which are used to characterise the impedance and reflections:

1. Voltage reflection coefficient (VRC)
2. Voltage standing wave ratio (VSWR)
3. Return loss calculator (RL)

1) Voltage Reflection coefficient (Γ) Calculator:

It is a ratio of the amplitude of the reflected wave to the wave incident at the junction. The reflection coefficient is denoted by the symbol gamma. The magnitude of the reflection coefficient does not depend on the length of the line, only the load impedance and the impedance of the transmission line.

The online calculators are available that calculates the reflection coefficient (Γ) by entering the value of the characteristic impedance Zo (in ohms) and load impedance ZL (in ohms).  This value varies from -1 (for short load) to +1 (for open load), and becomes 0 for matched impedance load.

Where,

V- = Amplitude of reflected wave in V

V+ = Amplitude of incident wave in V

Three factors are related to this effect: the magnitude of the impedance change, the rise time of the signal, and the delay of the signal on the narrow line.

2) VSWR Calculator:

VSWR (Voltage Standing Wave Ratio) is the measure of how efficiently RF power is transmitted into a load.  VSWR is the measure of how much signal gets reflected back into the system. It is the ratio between transmitted and reflected waves. A high VSWR indicates poor transmission-line efficiency and reflected energy. It varies from 1 to (plus) infinity.

3) Return loss (RL) Calculator:

Return Loss is an amount of power that is lost to the load and does not return into the system as a reflection. It is expressed in dB - A high return loss means more power is lost at the load. This is the dB value of absolute reflection coefficient. This loss value becomes 0 for 100% reflection and becomes infinite for ideal connection.

Return loss Calculator(by using VSWR):

Return loss Calculator(by using VRC):

JLCPCB Impedance Calculator Tool:

Transmission lines in PCB design may have some different formulas, so precise values for impedance matching are not easy to get with these software. The best thing is to contact the manufacturer and calculate the impedance from their calibrated impedance calculator tool.

The JLCPCB impedance calculator tool is an online resource provided by JLCPCB to help designers calculate the impedance of PCB traces. This tool is essential for designing high-frequency circuits where controlled impedance is critical for maintaining signal integrity.

Key Features:

1. Trace Type Selection: Choose between microstrip, stripline, or differential pairs.

2. Input Parameters: Enter the trace width, trace thickness, dielectric constant, and the distance between the trace and the reference plane.

3. Instant Calculations: The tool provides real-time calculations for characteristic impedance based on the input parameters.

4. Material Properties: It allows you to select different PCB materials, which affect the dielectric constant and the impedance.

Select the type of transmission line (e.g., microstrip or stripline), Enter the PCB material's dielectric constant. Input the trace width, thickness, and distance to the reference plane. The tool will calculate and display the impedance value. This tool is widely used in PCB design to ensure the impedance matches the required specifications, particularly in high-speed or RF circuits. You can access the JLCPCB impedance calculator through the website.