×2 vs ×4 vs ×8 vs ×16 RF Frequency Multiplier Phase Noise
How Do ×2, ×4, ×8 and ×16 RF Frequency Multipliers Affect Phase Noise?
RF frequency multiplication always increases phase noise.
For an ideal frequency multiplier with a multiplication factor of N, the input phase noise is degraded by:
20 × log10(N) dB
This means every frequency doubling increases phase noise by approximately 6 dB. Analog Devices also notes that all frequency multipliers degrade phase noise by at least 20log(N).
Phase Noise Increase by Multiplication Factor
| Multiplier | Ideal Phase Noise Increase |
|---|---|
| ×2 | +6.0 dB |
| ×4 | +12.0 dB |
| ×8 | +18.1 dB |
| ×16 | +24.1 dB |
So if the input oscillator has phase noise of:
-120 dBc/Hz at 100 kHz offset
the ideal multiplied output would be approximately:
| Multiplier | Output Phase Noise |
|---|---|
| ×2 | -114 dBc/Hz |
| ×4 | -108 dBc/Hz |
| ×8 | -102 dBc/Hz |
| ×16 | -96 dBc/Hz |
These values describe the theoretical multiplication of the source phase noise.
Why Does Frequency Multiplication Increase Phase Noise?
A frequency multiplier increases both the carrier frequency and the phase deviation of the input signal.
If the input phase fluctuation is multiplied by N, the corresponding phase-noise power increases by:
N²
Converting this to decibels gives:
10 log10(N²) = 20 log10(N)
That is why doubling the frequency results in approximately 6 dB worse phase noise.
What Happens With a ×2 Multiplier?
A ×2 multiplier introduces the smallest phase-noise penalty among these options.
Ideal degradation:
20 log10(2) ≈ 6 dB
For example:
Input: 5 GHz
Output: 10 GHz
Input phase noise: -120 dBc/Hz
Ideal output phase noise: approximately -114 dBc/Hz
×2 multipliers are therefore commonly used when relatively low phase-noise degradation is important.
What Happens With ×4 and ×8?
For ×4:
20 log10(4) ≈ 12 dB
For ×8:
20 log10(8) ≈ 18 dB
As the multiplication ratio increases, the quality of the input reference becomes increasingly important.
A mediocre oscillator may be acceptable before multiplication but may no longer meet the system phase-noise requirement after ×8 multiplication.
What Happens With a ×16 Multiplier?
A ×16 multiplier produces an ideal phase-noise increase of approximately:
24 dB
This is significant.
For example, if a 625 MHz source has phase noise of -120 dBc/Hz, the ideal phase noise after ×16 multiplication to 10 GHz would be approximately:
-96 dBc/Hz
This is why high-ratio multiplier chains usually require a very low-noise input reference.
Is the Real Phase Noise Exactly 20log(N) Worse?
Not necessarily.
The 20log(N) value describes the phase noise transferred from the input signal.
The multiplier itself also introduces additive phase noise.
Actual output phase noise therefore depends on:
Input oscillator phase noise
Multiplication factor
Multiplier additive phase noise
Bias noise
Device technology
Output frequency
Offset frequency
ADI specifically describes 20log(N) as the minimum degradation associated with multiplication.
Example: HMC445LP4E ×16 Multiplier
The HMC445LP4E is an active ×16 frequency multiplier with approximately:
Input frequency: 0.619–0.7 GHz
Output frequency: about 9.9–11.2 GHz
Output power: approximately +7 dBm
Subharmonic suppression: >25 dBc
Additive SSB phase noise: approximately -130 dBc/Hz at 100 kHz offset
ADI describes its low additive phase noise as useful for maintaining overall system noise performance in LO multiplier chains.
The important distinction is:
20log(N) degradation comes from multiplying the input source phase noise, while additive phase noise comes from the multiplier device itself.
Both must be considered in the final system design.
Is One ×16 Multiplier Better Than Several ×2 Stages?
From the ideal phase-noise multiplication rule alone, they are essentially equivalent.
Four ×2 stages give:
6 + 6 + 6 + 6 ≈ 24 dB
which is approximately the same theoretical degradation as one ×16 stage.
However, a real cascaded multiplier chain may introduce additional:
Additive phase noise
Gain variation
Harmonics
Subharmonics
Amplifier noise
Filter loss
The best architecture therefore depends on the available multiplier devices and required spectral purity.
Which Multiplication Ratio Should You Choose?
Use the lowest practical multiplication ratio when phase noise is critical.
A simple rule is:
×2: lowest phase-noise penalty
×4: moderate multiplication with about 12 dB degradation
×8: requires a cleaner input source
×16: compact high-ratio conversion, but input phase noise becomes much more critical
The multiplication ratio should be selected together with the required output frequency, phase-noise target, output power, and harmonic suppression.
Summary
Frequency multiplication increases source phase noise according to:
Phase Noise Increase = 20 log10(N)
Therefore:
×2 → about +6 dB
×4 → about +12 dB
×8 → about +18 dB
×16 → about +24 dB
Actual output phase noise can be worse because the frequency multiplier also contributes additive phase noise.
For low-phase-noise radar, microwave LO, Satcom, and test systems, start with the cleanest practical reference source and avoid unnecessary multiplication.
