by Jacob Trevithick

Phase noise is critical to systems, like Electronic Warfare and 5G Communications, requiring precise frequency stability. Oscillators are typically the determining factor in the signal chain’s phase noise performance. However, in extremely low phase noise systems, the amplifier phase noise contribution is considered. This tech note explores amplifier’s phase noise contribution, demonstrating:

- Amplifiers only contribute 1/f and White PM noise to a signal chain.
- 1/f noise is apparent at approximately 1‑100 kHz offset frequencies.
- Amplifier 1/f noise adds linearly in series and subtracts linearly in parallel.
- Oscillator higher order phase noise dominates at <1 kHz offset frequency.

## Phase Noise Regions

Typical phase noise measurements are divided into regions, each attributed to a different physical phenomenon. Figure 1 identifies the phase noise regions and their corresponding mechanisms, and displays typical oscillator and amplifier phase noise trends. High order (1/f4, 1/f3, and 1/f2) phase noise is caused by the cavity effects from oscillators, and are not contributed by amplifiers.

Figure 1: Typical oscillator and amplifier phase noise trends vs. offset frequency. Phase noise regions labeled with corresponding physical mechanisms.

In the article, Phase noise in RF and microwave amplifiers, by Rodolphe Boudot and Enrico Rubiola, amplifiers show a phase noise spectrum that follows 1/f noise trend and then a White PM noise floor. The amplifier’s White PM noise floor, b_{o}, is governed by,

where F is the large signal amplifier noise figure, k is the Boltzmann’s constant, *T _{o}* is the device temperature, and

*P*is the amplifier input power. The white noise contribution of a series of cascaded amplifiers can be calculated from Friis Formula.

_{o}Boudot and Rubiola also demonstrate that amplifiers contribute 1/f noise to a system’s phase noise by upconverting the intrinsic 1/f noise of the transistors. Cascaded amplifier 1/f phase noise adds linearly with each additional amplifier added to the chain. Therefore, the 1/f phase noise contribution will increase by +3 dB for each doubling of series amplifiers. Parallel amplifiers demonstrate a linear reduction in phase noise. Similarly corresponding to a decrease of -3 dB for each doubling of parallel amplifiers.

## Measurement Setups

Absolute and residual phase noise measurements are taken to demonstrate amplifier phase noise contributions to a low-phase noise system. The absolute measurements demonstrate the total phase noise of the signal chain, while the residual measurement is a measure of the amplifier’s phase noise contribution. The residual measurement cross correlates the oscillator’s phase noise out of the measurement using two internal mixers. The four absolute measurements and the residual measurement setups are shown below in figure 2 and figure 3, respectively. Attenuators are used in all cases to control the input powers into each amplifier. Controlling the compression levels in each amplifier is critical to the measurement because the noise figure characteristics are altered in compression, and consequently the phase noise performance is altered. In each case the source used is a Wenzel 501‑27134 crystal oscillator, and the amplifiers under test are identical ADM1‑0026PA units.

Figure 2: Oscillator Alone (Top left), Oscillator + amplifier (Top right), Oscillator + 2 amplifiers in series (middle), and Oscillator + 2 amplifiers in parallel (bottom).

Figure 3: Amplifier residual phase noise measurement setup.

## Phase Noise Measurements

Figure 3: Absolute phase noise measurements: Oscillator alone (Blue), Oscillator + Single Amplifier (Red), Oscillator + 2 Amplifiers in series (Black), Oscillator + 2 Amplifiers in parallel (Yellow). Amplifier residual phase noise measurement (Green).

Figure 3 verifies the results of Boudot and Rubiola. The low frequency higher order phase noise regions (<1 kHz offset) are dominated by the oscillator phase noise, and are not present in the amplifier residual measurement. The amplifier’s residual phase noise is ‑50 dB – ‑10 dB compared to the oscillator’s absolute phase noise in this region. Consequently, in the single, series, and parallel amplifier cases the measured phase noise below 1 kHz offset is indiscernible from the oscillator phase noise. This supports the claim that amplifiers do not add any higher order phase noise to this system.

When the amplifiers are added to the oscillator chain, a clear phase noise increase is shown at approximately 1 kHz – 100 kHz offset frequencies. The phase noise in this region demonstrates an approximate ‑10 dB/decade slope in all cases, which is the 1/f noise signature. The amplifier’s 1/f contribution begins to add phase noise to the absolute measurements at ~1 kHz – 5 kHz offset frequencies where the amplifier’s residual phase noise magnitude is within ~5 dB of the oscillator’s phase noise. Then, as the amplifier residual phase noise becomes greater in magnitude than the oscillator phase noise (~5 kHz – 100 kHz), the amplifier dominates the absolute measurements.

The phase noise value at 10 kHz offset is analyzed in the single, series, and parallel amplifier cases. The oscillator phase noise is linearly subtracted in each case to extract the contribution from the respective amplifier chain. Table 1 below shows the phase noise at 10 kHz offset and the corresponding difference between one amplifier and two amplifiers in series/parallel. The 2.9 dB phase noise increase from a single amplifier to two amplifiers in series is expected. The measured 2.0 dB decrease between the single and parallel cases is also within reason. A 3 dB reduction is only theoretical as it assumes lossless power dividers and identical input powers, gain, and noise figures. Therefore, it is expected to measure closer to 2‑2.5 dB reduction in practice.

Table 1: Single Amplifier and Cascaded Amplifier Phase noise adjusted for Oscillator noise floor, and corresponding increase at 10 kHz offset frequency.

Measurement | Single ADM1 | 2 ADM1s in series | 2 ADM1s in parallel |

Absolute Phase Noise at 10 kHz Offset, adjusted for Oscillator Phase noise (dBc/Hz) | ‑153.2 | ‑150.3 | ‑155.2 |

Delta from Single Amplifier Case | – | +2.9 dB |
‑2.0 dB |

The amplifier’s White PM noise floor contribution is not as significant as the 1/f noise contribution because it is ~5 dB below the oscillator’s noise floor. However, a 0.7 dB median increase at 500 kHz ‑ 1 MHz offset frequencies demonstrates the far‑off White PM noise floor increases when comparing the single and cascaded amplifier cases. Supporting the claim that amplifiers contribute White PM noise to the oscillator’s phase noise response.

## Key Takeaways

These measurements confirm to the reader that amplifiers contribute 1/f noise and far off white noise to a system’s phase noise, and no other higher order noise mechanisms. Amplifier’s 1/f noise adds linearly in series and is reduced linearly in parallel. Therefore, with *m *amplifiers in a chain, series 1/f phase noise increases by *+3log _{2}(m) dB*, and parallel 1/f phase noise decreases by

*-3log*. White noise adds according to the Friis formula. It is also worth mentioning that this measurement set is done using a very low phase noise oscillator, and that in practice, significantly low phase noise oscillators are necessary for the amplifier contribution to have any effect on the system’s phase noise performance.

_{2}(m) dBCheck out our full line of amplifiers here, including our new APM series low phase noise HBT amplifiers.

# Note: Previous Post

Below is the previous post attempting to prove/disprove amplifier 1/f phase noise contributions. As mentioned, the equipment used did not provide an adequately low noise floor. This resulted in the amplifier 1/f contribution to be unnoticeable in the phase noise measurements. With the new data taken above, it is clear the results regarding amplifier’s 1/f phase noise made in Boudot and Rubiola’s article are accurate and reproducible.

Phase noise, and amplifier noise in particular, has been a pet project of Ferenc’s for some time. This stems from the fact that, as I will detail in a future post, a passive silicon schottky diode mixer adds very little noise. Normally when customers find excess noise on a conversion it is because of LO noise transmitting to the IF/RF output. We found a recent article called “Phase Noise in RF and Microwave Amplifiers”, by Rodolphe Boudot and Enrico Rubiola (IEEE Trans. Ultrasonics, Ferroelectrics, and Frequency Control, vol. 59, no. 12, Dec. 2012) where they show plots of phase noise of an oscillator after amplification with different output powers. We decided to perform the same measurement. In our experiment we take a reference 80 MHz oscillator (a Wenzel low phase noise crystal) and measure the phase noise. Then we attenuate the signal by 50 dB and amplify it back up by 50 dB. The input noise floor is at -159.4 dBm/Hz, and the output is at 106.5 dBm/Hz. The noise floor increase is as a result of the amplification and noise figure of the amplifier. The phase noise plots are show below, along with an extra line showing the phase noise of the oscillator with a constant noise level equal to the noise floor of the amplifier added to it.

As you can see, there is very little difference between the phase noise of the amplified signal and the phase noise of the oscillator with white noise added to it. Hence the question, do amplifiers add flicker noise? In the frequency range near the carrier we see hardly any noise addition. This suggest that at a minimum, the flicker noise addition for the amplifier we used (a Centellax wideband amplifier similar to our T3 driver amps) is very low. So low that it’s hard for us to believe that it adds flicker noise at all.

CORRECTION (1/14/20)

When we originally performed this experiment, we were limited by the test equipment (an Agilent E4448A spectrum analyzer). Therefore we were unable to see the actual phase noise of the crystal since it was in the noise floor of the measurement. Prof. Rubiola helpfully provided a notation on our plot indicating where we would expect to see the phase noise power spectral density assuming that we had sensitive enough equipment:

As you can see from the plot, our noise floor was at least 10-15 dBc/Hz too high to measure the Wenzel oscillator or the amplifier. Indeed, our own measurements suggest that the noise floor is on the order of a standard amplifier such as the ADM-5974CH and 15 dB higher than a low phase noise amplifier such as the APM-6849.

We regret the error