What is the difference between PSMR and PSRR?

As we all know, to achieve low phase noise performance, especially ultra-low phase noise performance, a low-noise power supply must be used to achieve optimal performance. However, the literature does not detail how to quantify the impact of power supply noise voltage levels on phase noise through a systematic approach. This article aims to change that.

This paper proposes the power supply modulation ratio (PSMR) theory, which measures how power supply defects are modulated onto the RF carrier. This theory is verified by looking at the contribution of power supply noise to the RF amplifier phase noise; measurements show that this contribution can be calculated and predicted with reasonable accuracy. Based on this result, this paper also discusses a systematic approach to characterizing power supplies.

The power supply modulation ratio is similar to the well-known power supply rejection ratio (PSRR) , but with one key difference. PSRR is a measure of how much power supply imperfections are coupled directly into the device output. PSMR is a measure of how power supply imperfections (ripple and noise) are modulated onto the RF carrier.

The "Principles" section below introduces a transfer function H(s) that relates PSMR to power supply defects to quantitatively illustrate how 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 characterized, the power supply's phase noise and spurious contributions can be accurately predicted using the power supply's modulation ratio and based on the ripple and noise specifications in the power supply's data sheet.

Figure 1. Sinusoidal ripple on the power supply modulates onto the RF carrier creating spurious signals

Spurious levels are related to both the sine wave amplitude and the RF circuit sensitivity. 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 purposes of this discussion, H(s) is the transfer function from the power supply defect to the interfering 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 low-level modulation is available to simulate the effect of the power supply on the RF carrier.

The amplitude modulation of the signal can be written as

The amplitude modulation component m(t) can be written as

where f _m is the modulation frequency. The AM modulation level of the RF carrier can be directly related to the power supply ripple. The relationship is as follows:

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

Spurious levels can be calculated using amplitude modulation

The effect of the power supply on phase modulation can be written similarly. The phase modulated signal is

The phase modulation term is

Likewise, phase modulation can be directly related to the power supply as follows

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

To help visualize the spurious effects of m _rms and Ø _rms , Figure 2 shows the spurious level versus m _rms and Ø _rms .

Figure 2. Spurious level versus m rms _and Ø _rms

To summarize the above discussion, the ripple on the power supply is converted into the modulation terms m _rms and Ø _{rms of the root mean square voltage v rms} of the AC term of the power supply voltage . Hm (s) and HØ (s) are the transfer functions from v _rms to m _rms and Ø _{rms respectively.}

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

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

Likewise, if we consider a signal x(t) with phase modulation, then

In this case, Ø(t) is a noise term.

The power spectral density is defined as

Phase noise is defined in terms of power spectral density

Next, the same HØ (s) is applied to the phase noise for spurs resulting from phase modulation due to power supply ripple. In this case, HØ (s) is used to calculate the phase noise due to 1/f noise on the power supply.

Figure 4. Using the HMC589A amplifier to demonstrate PSMR principles

To characterize the power supply sensitivity, a sine wave is injected into the 5 V power supply. Sine waves produce spurious signals on the RF, which are measured in dBc. The spurious content is further decomposed into AM and PM components. Featuring Rohde & Schwarz FSWP26 phase noise analyzer and spectrum analyzer. AM and PM spurious levels are measured by AM and PM noise measurements respectively, and spurious measurements are enabled. Results are tabulated, test conditions are 3.2 GHz, RF input is 0 dBm.

Table 1. HMC589A Characterization Spurs vs. Supply Sine Wave Ripple, 3.2 GHz, 0 dBm Input Power

Test data shows that the power supply sensitivity of an RF amplifier 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 demonstrate the principle using amplifier characterization and measurements.

First, use a fairly noisy power supply. Measure noise density. The power supply contribution to phase noise is calculated based on the characterized HØ(s) and compared with the phase noise measurement. Measurements were taken using a Rhode & Schwarz FSWP26. Noise voltage is measured by baseband noise measurements. A measure of amplifier residual phase noise is measured using the test set's internal oscillator to measure additive phase noise. The test configuration is shown in Figure 5. In this configuration, oscillator noise is canceled in the mixer, and any unusual noise is eliminated in the cross-correlation algorithm. This allows the user to achieve very low level residual noise measurements.

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

The power supply noise, measured phase noise, and predicted power supply noise contribution are shown in Figure 6. It is clear that between 100 Hz and 100 kHz offset, the phase noise is dominated by the power supply, and the predictions about the power supply contribution are very accurate.

Figure 6. Technical verification using a high-noise power supply

Repeat the test with the other two power supplies. The results are shown in Figure 7. Likewise, the power supply's contribution to phase noise is completely predictable.

Figure 7. Validation of the technology with two additional power supplies

A common challenge in low phase noise device characterization is ensuring that measurements belong to the device and not to the surrounding environment. To eliminate power supply contributions from the measurement, an ADM7150 low-noise voltage regulator is used. The noise density quoted from the data sheet and the noise voltage measurements of the device used for phase noise testing are shown in Figure 8.

Figure 8. Noise voltage density of ADM7150 low-noise regulator

Table 2 lists a series of low-noise regulators and their key parameters. The devices presented here are ideally suited for powering RF components in low phase noise RF designs; see the data sheet for conditions and characteristics. 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 often limiting 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 families best suited for low phase noise RF designs

The results of the HMC589A residual phase noise test when powered from the ADM7150 are shown in Figure 9. This measurement shows the true performance of the amplifier with a noise floor below -170 dBc/Hz and this performance is maintained out to a 10 kHz offset.

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

Here's one way to quantitatively derive power supply specifications:

Calculate power supply noise specifications,

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

Figure 10. Changes in Hm (s) and HØ (s) versus offset frequency and power level, using HMC589A evaluation circuit at 3.2 GHz.