“Many radar systems require low phase noise to minimize clutter. High-performance radars need to pay special attention to phase noise, leading to a lot of design resources invested in reducing the phase noise of the frequency synthesizer and characterizing the phase noise of the frequency synthesizer components.

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Many radar systems require low phase noise to minimize clutter. High-performance radars need to pay special attention to phase noise, which has led to a lot of design resources being invested in reducing the phase noise of the frequency synthesizer and characterizing the phase noise of the frequency synthesizer components.

As we all know, in order to achieve low phase noise performance, especially ultra-low phase noise performance, a low-noise power supply must be used to achieve the best performance. However, the literature does not specify how to quantify the effect of power supply noise voltage level on phase noise through a systematic method. This article aims to change this situation.

This article proposes the power modulation ratio (PSMR) theory to measure how power defects are modulated onto the RF carrier. This theory is verified by the contribution of power supply noise to the phase noise of the RF amplifier; measurement results show that this contribution can be calculated and fairly accurately predicted. Based on this result, this article also discusses a systematic approach to describing power supply characteristics.

Introduction and definitions

The power modulation ratio is similar to the well-known power supply rejection ratio (PSRR), but there is one key difference. PSRR measures the degree to which power defects are directly coupled to the output of the device. PSMR measures how power imperfections (ripple and noise) are modulated onto the RF carrier.

The following “principle” part introduces a transfer function H(s) that associates PSMR with power supply defects to quantitatively explain how the power supply defects are modulated onto the carrier. H(s) has two components, amplitude and phase, which can vary with frequency and device operating conditions. Although there are many variables, once the characteristics are determined, the power supply modulation ratio can be used to accurately predict the phase noise and spurious contribution of the power supply according to the ripple and noise specifications in the power supply data sheet.

principle

Consider the ripple on the DC power supply used for RF devices. The power supply ripple is simulated by a sine wave signal, and its peak-to-peak voltage is centered on the DC output. The sine wave is modulated onto the RF carrier, generating spurious signals at a frequency offset equal to the frequency of the sine wave.

Figure 1. The sinusoidal ripple on the power supply is modulated to the RF carrier to generate spurious signals

The spurious level is related to the amplitude of the sine wave and the sensitivity of the RF circuit. Spurious signals can be further decomposed into amplitude modulation components and phase modulation components. The total spurious power level is equal to the spurious power of the amplitude modulation (AM) component plus the spurious power of the phase modulation (PM) component.

For the discussion here, H(s) is the transfer function from the power supply defect to the interference modulation term on the RF carrier. H(s) also has two components, AM and PM. The AM component of H(s) is Hm (s), and the PM component of H(s) is HØ (s). The following equation uses H(s) for actual RF measurements, assuming that low-level modulation can be used to simulate the impact of the power supply on the RF carrier.

The amplitude modulation of the signal can be written as

The amplitude modulation component m

Where fm is the AM modulation level of the modulating frequency RF carrier can be directly related to the power supply ripple, the relationship is as follows:

vrms is the root mean square value of the AC component of the power supply voltage. This is the key equation, which provides a mechanism for calculating the AM modulation of the RF carrier caused by the power supply ripple.

The spurious level can be calculated by amplitude modulation

Similarly, the influence of the power supply on the phase modulation can be written.The phase modulation signal is

The phase modulation term is

Similarly, the phase modulation can be directly related to the power supply, the relationship is as follows

The above formula provides a mechanism for calculating the PM modulation of the RF carrier caused by the power supply ripple.The spurious level caused by phase modulation is

To help visualize the spurious effects of mrms and Ørms, Figure 2 shows the relationship between the spurious level and mrms and Ørms.

Figure 2. The relationship between spurious level and mrms and Ørms

To summarize the above discussion, the ripple on the power supply is converted into the modulation terms mrms and Ørms of the root mean square voltage vrms of the AC term of the power supply voltage. Hm (s) and HØ (s) are the transfer functions from vrms to mrms and Ørms, respectively.

Now consider phase noise. Just as the sine wave is modulated onto the carrier to produce spurious signals, the 1/f voltage noise density will also be modulated onto the carrier to produce phase noise.

Figure 3. 1/f noise on the power supply is modulated onto the RF carrier to produce phase noise

Similarly, if we consider a signal x

In this case, Ø

The power spectral density is defined as

Phase noise is defined in terms of power spectral density

Next, apply the same HØ (s) to the phase noise for the spurs generated by the phase modulation caused by the power supply ripple. In this case, HØ (s) is used to calculate the phase noise generated by 1/f noise on the power supply.

Measurement example

To demonstrate the above principles, we characterized the power supply sensitivity and phase noise of the HMC589A RF amplifier, and measured these quantities using multiple power supplies. The HMC589A evaluation circuit used for characterization is shown in Figure 4.

Figure 4. Using HMC589A amplifier to demonstrate PSMR principle

In order to characterize the sensitivity of the power supply, a sine wave is injected into the 5 V power supply. The sine wave generates spurious signals on RF, and the magnitude of the spurious signals is measured in dBc. The spurious content is further decomposed into AM and PM components. Using Rohde & Schwarz FSWP26 phase noise analyzer and spectrum analyzer. The AM and PM spurious levels are measured by AM and PM noise measurements, respectively, and the spurious measurement is enabled. The results are tabulated. The test conditions are 3.2 GHz and the RF input is 0 dBm.

Table 1. HMC589A characterizes the relationship between spurs and power supply sine ripple, 3.2 GHz, 0 dBm input power

Test data show that the power supply sensitivity of RF amplifiers can be measured empirically using sine wave modulation, and the results can be used to predict the contribution of power supply noise to phase noise. More generally, this can be extended to any RF device. Here we use amplifier characterization and measurement to demonstrate the principle.

First, use a very noisy power supply. Measure the noise density. Calculate the contribution of the power supply to the phase noise based on the HØ (s) of the characterization and compare it with the measured value of the phase noise. Use Rhode & Schwarz FSWP26 for measurement. The noise voltage is measured by baseband noise measurement. The internal oscillator of the test device is used to measure the additive phase noise to measure the residual phase noise of the amplifier. The test configuration is shown in Figure 5. In this configuration, oscillator noise is eliminated in the mixer, and any unusual noise is eliminated in the cross-correlation algorithm. In this way, users can achieve very low-level residual noise measurements.

Figure 5. Amplifier residual phase noise test setup using cross-correlation method

Power supply noise, measured phase noise, and predicted power supply noise contribution are shown in Figure 6. Obviously, between 100 Hz and 100 kHz offset, the phase noise is mainly determined by the power supply, and the prediction of the power supply’s contribution is very accurate.

Figure 6. Technical verification using high-noise power supplies

Repeat the test with the other two power supplies. The result is shown in Figure 7. Similarly, the contribution of the power supply to the phase noise is completely predictable.

Figure 7. Verify the technology with two other power supplies

A common challenge in the characterization of low phase noise devices is to ensure that the measurement results belong to the device and not the surrounding environment. In order to eliminate the power contribution in the measurement, an ADM7150 low-noise regulator is used. The noise density quoted from the data sheet and the noise voltage measurement results of the device used for phase noise testing are shown in Figure 8.

Figure 8. The noise voltage density of the ADM7150 low-noise regulator

Table 2 lists a series of low-noise regulators and their key parameters. The devices given here are very suitable for powering RF devices in low phase noise RF designs; please refer to the data sheet for relevant conditions and characteristic curves. The data sheet includes noise density and PSRR curves at multiple offset frequencies. The table shows the noise density at 10 kHz offset, because this area is usually limited for many regulators. The PSRR shown corresponds to a 1 MHz offset, because many linear regulators lose rejection at these offsets and require additional filtering.

Table 2. Low-noise regulator series are most suitable for low-phase noise RF designs

When power is supplied from ADM7150, the result of HMC589A residual phase noise test is shown in Figure 9. The measurement result shows the real performance of the amplifier, the noise floor is lower than -170 dBc/Hz, and this performance has been maintained to a 10 kHz offset.

Figure 9. HMC589A residual phase noise, 3.2 GHz, input RF power of 0 dBm, ADM7150 regulator provides DC power

A systematic method to describe power supply characteristics

The power supply design for low phase noise applications usually chooses the best voltage regulation solution available without consideration, and ignores the actual minimum specifications, which can lead to over-design. For low-volume designs, this approach may be worth continuing, but for high-volume production, performance, cost, and complexity must be optimized, and over-designing may be an unwelcome waste.

The following is a method of quantitatively deriving power supply specifications:

The power supply is modulated with a sine wave to characterize H(s). H(s) will be a function of frequency and will be tested every decade.

Distribute the contribution of power to stray and phase noise, leaving a certain margin under the RF specification.

Calculate the power supply ripple specification,

・

Calculate the power supply noise specification,

An important thing in the first step above is to understand how Hm (s) and HØ (s) change under the expected working conditions of the design. In the HMC589A characterization, this change is measured at several power levels, as shown in Figure 10.

Figure 10. The relationship between the changes of Hm (s) and HØ (s) and the offset frequency and power level, using the HMC589A evaluation circuit with a frequency of 3.2 GHz

Concluding remarks

Although it is generally believed that power supply ripple and noise should be limited in RF applications, few people fully understand their quantitative effects. Using the systematic approach described in this article, engineers can step by step to quantify the impact of the power supply on the desired RF performance, so as to make wise power supply choices.