**Amplifiers/Converters??**

# A guide to better EMC for PCB design

**Keywords:rf?
microwave theory?
emc?
pcb?
**

**By John BerrieZuken Technology Center**

Complicated RF and microwave theory is useful for designing radio equipment, but digital designers aim to avoid turning circuits into radios without the benefit of an RF engineering degree. In digital design, the number of possible coupling routes is simply too large to deal with using analysis alone, because digital PCBs are not designed as closed RF systems. On the other hand, stating design rules out of context often presents an incomplete picture.

We are used to analyzing digital signals in the time domain, but this is not always suitable for EMC. With every new gigabit per second and faster-switching transceiver come their analog hitchhikers, higher-frequency sine waves. This article presents the first lines of defense against PCB-level EMC problems. Sine waves and their consequences form the backbone, and appear as Key Concepts followed by a brief introduction to how unintentional antennas can be created during PCB design.

**Key Concepts Explained**

EMC issues involve resonance, tuning and antennas, all of these being frequency-dependent. The frequencies of concern are those of sine waves which, when added together, form the many and varied signals in a design.

*Sine Wave Basics*

Sine waves are the purest kind of AC waveform. They can be generated by a pointer rotating anticlockwise from the reference axis within a circle, as shown in Key Concept 1. Each time the pointer rotates through 2p radians, or 360 degrees, the wave completes one cycle.

The number of times this happens in one second is the frequency. If a sine wave begins its cycle at time zero, then its amplitude at any point is Asin(?t), where A is the peak amplitude (the radius of the generating circle), t is the time and ? is the angular velocity. Angular velocity is the rate at which the angle of the sine wave changes in radians per second; its value is 2pf where f is the frequency.

**Key Concept 1: Sine Wave**

*Key facts*

- The rotating radius on the left represents the change in angle.
- The pointer rotates anticlockwise at a constant rate to generate the sine wave as shown.
- Angle changes by radians/second (the angular velocity).
- A sine wave can represent any quantity such as voltage, current or power.

*Key formulas*

- ? = 2pf where f is the frequency in Hertz
- Amplitude Y(t) = A sin(t) where A is the peak amplitude and t is time in seconds

*Adding sine waves*

Sine waves can be added together by summing the amplitudes of each wave at each point in time. The example shown in Key Concept 2 serves to demonstrate the principle.

Sine waves can be summed as vectors, where the angles of the vectors relative to the reference axis represent their starting angle. The starting angle of the sine wave shown in Key Concept 1 is zero. Luckily, in practice, sine waves can easily be summed automatically.

**Key Concept 2: Adding Sine Waves**

*Key facts*

Sine waves can be added as vectors, considering amplitude and phase angle.

*Key formulas*

Since B lags A by p/2 radians, these two waveforms are described by Asin(t) and Bsin(t-p/2).

**Content of a square wave**

The square wave illustrated in Key Concept 3 is probably the easiest wave shape to understand in terms of frequency content, and is also an idealized version of a very common type of clock signal (50% duty cycle). In reality, of course, the rise and fall times of a signal must be finite rather than zero and there is inevitably some distortion！both of these affect the frequency content to some degree.

It can seem artificial to construct waveforms in this way, but luckily it makes no difference whether or not the frequency domain represents an underlying truth or whether it is a purely mathematical construction. Like all engineering, and even science, the frequency domain is a model of reality that allows us to make predictions and build things that work. Electronic circuits, and, more importantly for our purposes, electric and magnetic fields, behave consistently with this model.

**Key Concept 3: Square Wave Composition**

*Key facts*

- Digital waveforms can be reconstructed by adding together harmonics of the right amplitude and phase angle to describe a signal in the frequency domain.
- Harmonics are integer multiples of the fundamental frequency.
- A square wave as shown is the sum of the fundamental and all odd harmonics.

The transformation into the frequency domain in terms of sines and cosines, known as the Fourier Transform, works well for square waves: in fact all the components are sines and all are odd harmonics. Odd harmonics are merely odd-number multiples of the fundamental frequency (the frequency of the digital square wave).

Once a waveform has been transformed into the frequency domain, the result can be viewed as a spectrum, where frequency is plotted along the horizontal axis, and amplitude vertically. In the case of the square wave, the result is shown in Key Concept 4.

Here, there is simply one value for each odd harmonic with the amplitude decreasing as the frequency increases. Since the scales are logarithmic, the decrease in amplitude seems less dramatic than it actually is (one, one third, one fifth and so on). To reconstruct a square wave perfectly requires an infinite number of odd harmonics, but in practice there is, of course, a law of diminishing returns when the amplitudes of higher-frequency harmonics become insignificant.

**Key Concept 4: Arbitrary Wave Frequency Spectrum**

*Key facts*

- RMS (Root Mean Square) values are often considered, as in this diagram. The RMS value of a sinusoidal voltage is simply the DC voltage that would dissipate the same power in a purely resistive load.
- Frequency spectra are often, as here, shown on a logarithmic scale.
- The units of frequency and amplitude do not matter. Fundamental frequency could just as easily be 1GHz as 1MHz, and amplitude Amperes or Microwatts.

**Content of arbitrary wave shapes**

In a complex PCB with many buses, clocks, control signals, and in some cases analog circuits, the wave shapes are diverse and not so easily expressed in the frequency domain as the ideal square wave. The original Fourier Transform was a transformation of a function, but what function does a waveform such as that in Key Concept 5 represent?

Problems like this led to the development of the DFT (Discrete Fourier Transform), which works by sampling. The trouble with the DFT is that it required order N2 calculations for N samples. Back in the nineteen-sixties, Tookey and Cooley found a more efficient method requiring only order Nlog2N calculations: The FFT (Fast Fourier Transform). It is this useful algorithm that forms the basis of much high-frequency analysis software.

**Key Concept 5: Arbitrary Wave Frequency Spectrum**

*Key facts*

- >
- In the general case, the components of the waveform show wide variations in both frequency and phase.
- This waveform has been solved with a FTT (Fast Fourier Transform) to yield its content in the frequency domain.

**Antennas by other names**

As far as radiated emissions and susceptibility are concerned, the main problem is one of unintentional antennas. Electromagnetic fields do not care whether you call it a power plane or a signal trace or a cutout. If a feature resonates at one of the major frequencies in your design it will generate electro-magnetic interference (EMI); if it resonates at one of the major frequencies in the fields in its environment, if will pick up EMI.

*Dipoles*

The simplest kind of antenna is a dipole, so-called because it is in two parts. The feed is in the center and the overall length is half a wavelength or an odd multiple of it as shown in Figure 1.

Figure 1！The dipole antenna works by resonating at a specific frequency. It radiates to a lesser extent at nearby frequencies.

So how could you get a dipole in a PCB design? One of the most common ways this can happen is by cabling similar to that in Figure 2.

Figure 2！PCBs and cables can look like dipoles.

In this case, if practicable, you could achieve a major EMC improvement by attaching cables at the same end of the PCB rather than at opposite ends.

*Slots and loop antennas*

Slots in planes also behave as antennas and are equivalent to dipoles but with different polarization. There are two prime candidates for slot antennas: enclosures and power/ground planes.

For enclosures the behavior is complex, as internal dimensions of the case and positions of parts within it all contribute to its shielding effectiveness. The key point for EMC is that where there is a choice between slots and small apertures, the latter are preferred.

In the case of slots in power planes, the rule is to avoid them as much as possible for any one power or ground reference. Not only can slots be tuned to a dangerous frequency, but they have a more common and direct consequence: they interrupt return current.

When a signal is transmitted over signal traces, the current has to return to its source. If your design has power and ground planes, then one or more of these generally acts as the return path. If a slot gets in the way, the current has to go all the way around, and this creates a larger loop.

Figure 3！Radiation is proportional to the square of the frequency times the area. Area should therefore be kept to a minimum.

**First Lines of defense***Layer stack*

The number one EMC enhancer is a good layer stack as shown in Figure 4. The capacitance in question is between ground planes and power planes or signal traces. Capacitance between ground and power planes lowers the impedance of the power system and provides a great deal of free decoupling.

Placing power and ground planes adjacent to each other supplements the decoupling capacitors that engineers put on the schematic by AC coupling fast power transients to ground. Expressing the total capacitance between the split power plane and ground plane by the basic plate capacitor equation as in Figure 4 is a major simplification, but serves to express the situation.

Figure 4！It makes sense to close-couple primary power and ground planes.

In Figure 4, the bulk high-speed tracking is on inner balanced stripline layers with opposite routing bias. Most crosstalk on PCBs is caused by parallel traces and EMC problems can be amplified when on-board crosstalk is transmitted onto cables or vice-versa.

Crosstalk between parallel runs on adjacent layers is particularly severe, so it is easy to see why this arrangement is so effective. If there are more than two signal layers without an intervening ground or power plane, signal integrity, and therefore also EMC, is downgraded due to excessive trace-to-trace coupling.

Ground and power planes, when referenced to chassis ground, help to shield high-speed traces from the outside world. The type of stack shown in Figure 4 takes advantage of this by protecting the bulk routing from its environment. Traces on outer layers are mainly for surface mount connections and should be kept as short as possible.

If you are designing a four-layer, two-signal plus power and ground layer board, this might lead you to place the power and ground planes on the two outer layers. My own preference in this is still to use the two central layers for power and ground to decouple the power supply and route on the outer layers. Manufacturing issues and the fact that the power and ground layers tend to get cut up and become less effective or even counter-productive for EMC, are major factors supporting this recommendation.

Referring to Figure 3 and the section titled Slots and loop antennas, the first power and ground planes encountered above and below signal traces must belong to the driving components' power supply to keep loop areas small, and to avoid return currents being diverted around slots.

It is essential for signal integrity to partition the design so that, for example, analog and digital areas are kept separate. For EMC it is worth remembering that shared power means shared noise; if a high-frequency operational amplifier has a gain of 10,000, then 1mV of noise theoretically becomes 10V.

**Differential signaling**

The number of differential pairs in each design seems to multiply month by month. Quite apart from their signaling properties, differential pairs greatly assist EMC. Since the signals are complementary, and, in closely-coupled pairs, referenced to each other, most radiated noise is cancelled out for the small loop area that remains.

Like other PCB traces, those used to form differential pairs are antennas and pick up noise; but since the noise on two closely-coupled traces tends to be of similar phase and amplitude, it is rejected at the receiver. Popular DDR (double data rate) memories have differential clocks that waste-consciously perform operations on both differential transitions.

**Reducing distortion**

As seen in Key Concept 5, high-speed signal edges contain high frequencies at a range of amplitudes. Provided signals meet their setup times, it is in our interests to cut down the higher frequencies so they do not radiate. The classic electronics solution to this problem is the Low Pass Filter.

It is relatively unusual to include specific low-pass filters in digital circuits, but topology (the order in which connections are routed) and termination style have a major effect. Topology control and appropriate termination are needed for signal integrity, and have useful spin-off benefits for EMC. Just as the best way to find out how effective terminations are for signal integrity is to simulate in the time domain, the best way to evaluate their effectiveness in cutting high frequency content is to transform the result into the frequency domain.

In Figure 5 the time domain receiver voltage and frequency domain receiver current are plotted with no planned topology or termination, compared with a far-end-branched topology with 47O series termination. The spectrum becomes far more regular, with large cuts in higher-frequency content.

Figure 5！Terminating this clock net with a 47O series resistor and branching to receivers at the far end cuts the high-frequency currents.

**Summary**

Even a basic appreciation of the frequency domain helps get high-speed digital designs right first time for EMC more of the time. The 80/20 rule of the vital few versus the trivial many applies as much here as to the rest of engineering.

**E-Bibliography**

- Phasor Diagrams, Kwantlen University College.
- PCB Design Guidelines, Infineon.
- Curbing the Power of Radiated EMI In ASIC Designs, Evaluation Engineering.
- Slot, notch, and rectangular loop antennas, Surrey University.
- Understanding and Finding the Invisible Antennas in your Design, Henry Ott Consultants.
- Analysis on the Effectiveness of Printed Circuit Board Edge Termination using Discrete Components Instead of Implementing the 20h Rule, Montrose Compliance, Institute of High-Performance Computing.
- Intermediate Level Modeling for EMC, York University.
- Fourier Series Approximation of a Square Wave, Connexions.
- Types of Antenna, St. Andrews University.

**About the authorJohn Berrie** is a Technology Partner with Zuken Technology Center, Bristol, UK. He is a veteran of signal integrity and EMC and the author of many papers and articles on that subject. He has played a major role in development of high-speed design EDA solutions for over 20 years as well as regularly being directly involved in high-speed hardware design.

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