Understanding Frequency Spread Spectrum in SMPS Designs

The rise of vehicle electrification requires solutions with efficient and powerful power conversion. These solutions are expected to have small form factors for power supplies. Having excellent efficiency and a small form factor requires high switching frequencies and fast switching flanks on the switching point of the switch-mode power supply (SMPS). This poses significant challenges for engineers.

 

Image used courtesy of Adobe Stock

 

Modern passenger vehicles are not only made to carry passengers from one destination to the next — they must also function as communication tools, TVs, home cinema sets, LED illumination centers, and even massage parlors. The customer’s focus is changing from purely driving characteristics (e.g., horsepower and acceleration) to entertainment systems, such as the size of multimedia touchscreens and the ability to access mobile networks.

The vehicle of tomorrow must be able to connect to social media, stream UHD videos, and keep passengers online, as well as communicate with other vehicles, infrastructure, and pedestrians to enable autonomous driving. On top of that, these cars must maintain older features such as classic electrical control units (ECUs) for features like radio tuners and GPS navigation. This leads to a rising number of ECUs.

 

Understanding Frequency Spread Spectrum

To understand how FSS works, let’s look at the spectrum of a traditional SMPS like the MPQ4371-AEC1. The MPQ4371-AEC1 is an automotive buck regulator that can achieve up to 11 A of continuous output current (I_OUT) with zero-delay PWM (ZDP) control and a switching frequency (f_SW) up to 2.5 MHz.

Figure 1 shows the spectrum of this SMPS when the main f_SW is set to 2.2MHz. The corresponding harmonics can be calculated as (n x f_SW), where n is the corresponding harmonic.

 

Figure 1. Spectrum of a traditional SMPS when f_SW = 2.2 MHz. Image used courtesy of Monolithic Power Systems

 

The power of the harmonics decreases with higher measurement frequencies, and it disappears in the noise floor at about 400 MHz. Each peak in the spectrum (calculated n x f_SW) is shown with the resolution bandwidth (RBW) and the filter type used by the spectrum analyzer.

The RBW filter is defined by the minimum and maximum frequency, as well as the filter order. RBW determines the settling time (t_S) for the RBW filter, calculated with Equation (1):

\[t_{s}=\frac{1}{RBW}\,\,\,\,\,(1)\]

Figure 2 shows a traditional RBW filter of a spectrum or signal analyzer.

 

Figure 2. The RBW filter has certain characteristics, such as bandwidth. Image used courtesy of Monolithic Power Systems

 

The spectrum analyzer sweeps through the defined frequency area by measuring a spectrum. Whenever there is a peak inside the RBW filter, this specific frequency is shown in the scope (see Figure 3). This allows moving power from each specific harmonic inside the area between the peaks.

 

Figure 3. There is a certain resolution bandwidth filter and switching frequency within every spectral area. Image used courtesy of Monolithic Power Systems

 

Figure 3 shows that a higher RBW combined with a smaller f_SW will move the spectrum closer together, meaning the energy of the harmonics can only be transferred to a smaller area. Theoretically, if all the energy of the peaks is transferred into white noise, the attenuation (α) of each specific peak is linked to f_SW and RBW, estimated with Equation (2):

\[\alpha=10\times log\Bigg(\frac{RBW}{f_{SW}}\Bigg)\,\,\,\,\,(2)\]

The relationship between the maximum theoretical attenuation achieved via FSS and the corresponding RBW and f_SW is shown in Figure 4. For example, assume that the SMPS’ f_SW is 0.5 MHz, and the RBW is 120 kHz; the maximum attenuation achieved with FSS is 6.2 dB.

 

fSW[MHZ]	Attenuation for RBW[dB]
	9kHz	120kHz	1000kHz
0.1	10.5	0.0	0.0
0.2	13.5	2.2	0.0
0.3	15.2	4.0	0.0
0.5	17.4	6.2	0.0
1	20.5	9.2	0.0
2	23.5	12.2	3.0
5	27.4	16.2	7.0
10	30.5	19.2	10.0
100	40.5	29.2	20.0

Figure 4. The maximum possible theoretical attenuation for FSS changes depends on f_SW. Image used courtesy of Monolithic Power Systems

 

Transforming a Specific Spectrum to FSS

We must dither around the original switching frequency to transform the SMPS’ original spectrum to FSS. 

To dither around the original switching frequency, consider the following:

1. t_S: The RBW’s settling time must be considered. If the time for the frequency to change (the modulation frequency, or f_MOD) is longer than t_S, there is no achievable attenuation with FSS.

2. RBW: If the dither frequency (f_SPAN) is smaller than the RBW, the frequency dithers within the filter’s bandwidth, and the attenuation with FSS is zero.

When considering the two rules above, it can be concluded that f_SPAN must exceed the RBW, calculated with Equation (3): 

\[f_{SPAN}>RBW\,\,\,\,\,(3)\]

Meanwhile, f_MOD must exceed the inverse of t_S, estimated with Equation (4):

\[f_{MOD}>\frac{1}{t_{s}},\,\,\,\,\,with\,\,\,\,\,t_{s}=\frac{1}{RBW}\,\,\,\,\,(4)\]

The frequency change (f_SPAN x f_MOD) can be calculated with Equation (5):

\[Frequency\,Change=f_{SPAN}\times f_{MOD}>RBW^{2}\,\,\,\Big[\frac{Hz}{s}\Big]\,\,\,\,\,(5)\]

Table 1 shows the frequency change values to achieve FSS within specific RBWs.

 

Table 1. Frequency Changes to Achieve Attenuation

RBW	Settling Time	Minimum Frequency Change
9 kHz	111 µs	81 MHz/s
120 kHz	8.33 µs	14.4 GHz/s
1000 kHz	1 µs	1 THz/s

 

To generate a white noise signal and be compliant with the two rules above, we need to dither from zero to infinity within a period very close to zero. As this is technically impossible, the dither frequency (f_SPAN) should be between 10% and 20% of the original f_SW. This will provide enough f_SPAN to ensure a good attenuation and keep the SMPS at a stable operating point. 

Real measurements show that the attenuation with FSS is most effective when the modulation frequency (f_MOD) is almost equal to the spectrum analyzer’s RBW.

For example, consider a scenario where f_SW is 2 MHz and f_SPAN is 20%. Table 2 shows f_MOD and the frequency change for this scenario.

 

Table 2. Frequency Change for Given Working Areas

Modulation Frequency (fMOD)	Frequency Change
9 kHz	3.6 GHz/s
120 kHz	48 GHz/s

 

By comparing Tables 1 and 2, you can see it is possible to achieve great attenuation for an RWB of 9 kHz with an f_MOD of 9 kHz. However, the attenuation with an RBW of 120 kHz is 0 since the frequency change is too slow. To achieve reasonable attenuation for a 120 kHz RBW, we must increase the FSS frequency.

Because FSS is always modulated to the SMPS switching frequency, high harmonics will automatically reach a high-frequency change at their dedicated frequency (see Table 3).

 

Table 3. Corresponding Frequency Change for the SMPS’s Harmonics

Harmonic	Spectral Frequency	fMOD	fSPAN (20%)	Frequency Change
fSW	2 MHz	9 kHz	400 kHz	3.6 GHz/s
Second harmonic	4 MHz	9 kHz	800 kHz	7.2 GHz/s
Third harmonic	6 MHz	9 kHz	1200 kHz	10.8 GHz/s
Fourth harmonic	8 MHz	9 kHz	1600 kHz	14.4 GHz/s

 

Modulation Waveforms

We can consider the modulation waveform after establishing the correlation between f_MOD and f_SPAN. Because the frequency change during normal operation should be linear, using a triangular modulation signal is the easiest way to modulate FSS (see Figure 5). This is simple to implement, but at the signal’s edges, the frequency change within a specific timeframe is half the frequency change during the rising or falling flank (f/2). 

To prevent this, it is possible to use a sawtooth waveform, where the frequency change is linear while ramping. After receiving the maximum f_SW, the SMPS changes from the maximum to the minimum f_SW within one switching cycle. However, this can cause control loop instability and output voltage (V_OUT) undershoot or overshoot. 

Therefore, mixing different waveforms (e.g., the Hershey’s Kiss waveform or a stepped triangular waveform) can optimize attenuation while maintaining SMPS stability. 

Figure 5 shows the different FSS modulation waveforms.

 

Figure 5. The modulation signal for FSS can be shown to include f_SPAN and f_MOD. Image used courtesy of Monolithic Power Systems

 

These waveforms have one thing in common: They can only be used with one specific modulation frequency (f_MOD).

From the rules in the paragraph above, f_MOD should be within the frequency area of the RBW to achieve the best possible attenuation. When checking the CISPR 25 norm, there are two very critical frequency areas for SMPS developers:

1. The rod-antenna measurement, which goes from 150 kHz to 30 MHz with an RBW of 9 kHz.

2. The biconical-antenna measurement, which goes from 30 MHz to 300 MHz and has its toughest limits with an RBW of 120 kHz.

 

Figure 6. There are different FSS modulation waveforms to optimize attenuation. Image used courtesy of Monolithic Power Systems

 

These two measurements use two different RBWs, so the FSS f_MOD can only be optimized for one specific frequency area.

To optimize FSS for the full spectrum, the MPQ4371-AEC1 offers dual-FSS modulation (see Figure 7).

 

Figure 7. The MPQ4371-AEC1 features a dual-FSS modulation waveform. Image used courtesy of Monolithic Power Systems

 

Using this modulation waveform provides the benefits of FSS within the low-frequency (LF) and high-frequency (HF) spectrum. The main carrier (f_MOD(LF)) has a frequency of 15kHz, which is optimized to achieve an attenuation on the SMPS spectrum with the rod-antenna measurement. Ideally, f_MOD(LF) should have a frequency of 9kHz, but this frequency can cause audible noise from the SMPS. To avoid this, f_MOD(LF) can be increased to 15kHz. This gives nearly the same attenuation as the 9kHz modulation frequency and avoids audible noise. The second frequency is modulated on the carrier frequency with 120kHz, providing additional attenuation for the biconical antenna measurement. Using dual-FSS modulation allows for tuning the specific modulation frequency’s f_SPAN for each given use case. The MPQ4371-AEC1 provides eight different FSS options for further fine-tuning (see Table 4).

 

Table 4. FSS Options for the MPQ4371-AEC1

fSPAN Options	fMOD(LF) (15kHz)	fMOD(HF) (120kHz)
fSPAN 1	-	-
fSPAN 2	10%	-
fSPAN 3	6.2%	-
fSPAN 4	8.6%	2.5%
fSPAN 5	6.2%	2.5%
fSPAN 6	6.2%	4.3%
fSPAN 7	4.8%	2.5%
fSPAN 8	4.8%	4.3%

 

Practical Measurements

To show the effects of the different types of FSS, we can compare different versions of the MPQ4371-AEC1 on a real evaluation board with identical settings. The standard evaluation board for the MPQ4371-AEC1 was used in a CISPR 25 EMC chamber, and the measured frequency range was between 150kHz and 1GHz. To compare the effects of FSS, three modes were tested:

• The MPQ4371-AEC1 without FSS (green trace)
• The MPQ4371-AEC1 with 15kHz FSS and a ±10% span (blue trace)
• The MPQ4371-AEC1 with dual-FSS: 15kHz FSS and a ±6.2% span, and 120kHz FSS with a ±2.5% span (yellow trace)

The MPQ4371 ran with a 2.2 MHz f_SW and a 3 A load in all three scenarios. Figure 8 shows the measurements captured via the rod-antenna method with an RBW of 9 kHz.

 

Figure 8. It is possible to take the EMC measurements for rod-antenna FSS. Image used courtesy of Monolithic Power Systems

 

Figure 9 shows the EMC spectrum in the frequency area between 30MHz and 1GHz with an RBW of 120kHz.

 

Figure 9. It is possible to take the EMC measurements for biconical and log-periodic FSS. Image used courtesy of Monolithic Power Systems

 

Figure 8 and Figure 9 show that FSS can make a huge difference in the SMPS frequency spectrum. Especially for the rod-antenna measurement, FSS can effectively reduce the peaks at the fundamental switching frequency and the first harmonics. In this scenario, a maximum attenuation of 14dB is achieved. 

For the rod-antenna measurement, the single 15kHz FSS is more effective than the dual-FSS method since the frequency span is bigger for that modulation (10% with single-FSS vs. 6.2% with dual-FSS). 

However, higher frequencies benefit from the dual-FSS method, especially in the 40 to 140 MHz range. Dual-FSS provides an additional benefit of up to 3 dB since f_MOD stays within the RBW.

 

Frequency Spread Spectrum Takeaways

Frequency spread spectrum is an effective method to attenuate the spectrum of an SMPS. Care must be taken regarding the modulation frequency and the frequency span—two critical limitations that can result in no attenuation. In addition, the modulation waveform plays a role since using single-FSS or dual-FSS influences different frequency areas. In contrast, each specific waveform (e.g., triangular or sawtooth) also influences the stability of the SMPS.

Ultimately, using FSS should be a case-by-case decision. FSS should be tuned so that the most sensitive frequency areas provide the most attenuation within the SMPS spectrum, making devices such as the MPQ4371-AEC1 ideal, providing up to eight FSS options. Visit MPS to find an automotive-grade step-down converter to meet your design needs.