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All electronic components contribute to phase noise, but oscillators are generally the dominant source. A voltage-controlled oscillator (VCO), whether free-running or phase-locked, incurs phase noise as a consequence of noise modulation. Phase-noise specifications characterize spectral purity. The output of an ideal oscillator, for instance, would be a pure sinusoid represented in the frequency domain as a single-frequency vertical line. Actual oscillators include noise sources that cause the output frequency to deviate from its ideal position, producing a “skirt” of unwanted frequencies near the carrier.

You can intentionally generate or worsen phase noise in two ways: One is to directly modulate the oscillator or VCO using a noise source. A VCO (Figure 1a) is phase-locked with a phase-locked loop (PLL), and the loop filter's bandwidth is set lower than the minimum modulating frequency. If, for example, the minimum phase-noise offset frequency of interest is 10 Hz (from the carrier), set the PLL loop bandwidth to 1 Hz. You inject noise directly into the VCO's frequency-tuning input, where it modulates the VCO to produce phase noise at the output. Then, you can increase the phase-noise level by increasing the input noise-density level.

The output phase noise is shaped by the VCO gain (K_VCO). Suppose the VCO frequency is ƒ₀ and is modulated by a noise source of V_n(ƒ_n) in a bandwidth of 1 Hz at frequency ƒ_n. Using a narrowband approximation for frequency modulation¹, the VCO output is

The first term represents the carrier signal, and the second term represents noise power at a ±ƒ_n offset from the carrier. Phase noise is defined as the ratio of noise power at the ƒ_n offset to the carrier power at ƒ₀:

Remember that V_n(ƒ_n) is the rms noise voltage in a 1 Hz bandwidth at ƒ_n. The phase noise profile is the noise source profile divided by ƒ_n. Thus, for a white-noise input source with flat noise-density profile modulating the VCO (V_n(ƒ_n) = constant), the output phase noise profile decreases 20 dB/decade as shown in Figure 2 (assuming the induced phase noise is much greater than the VCO's intrinsic phase noise).

Another method for producing phase noise uses a phase modulator to modulate the carrier signal at the phase-locked VCO output (Figure 1b). This approach injects noise into the phase modulator, which is a lowpass filter in the LCL configuration². The two inductors are fixed, and the capacitance is made variable using a varactor diode, set to a nominal level of capacitance by the application of reverse bias. Noise voltage across the varactor varies the capacitance, which in turn varies the phase. Thus, the noise voltage is translated into phase noise. Increasing the noise voltage increases the level of phase noise. The phase-modulator method does not restrict the PLL loop bandwidth, which can, therefore, be as wide as necessary to achieve a faster lock time. As another advantage, the phase-noise profile depends not on the VCO gain, but on the phase gain (K_PHASE), in units of radians per volt. Phase gain depends on the phase response of the LCL filter and the varactor-diode capacitance characteristics. Thus, the VCO output following the phase modulator is

where V_n(t) is the noise voltage at time t. The phase-noise term is K_PHASEnV_nt=φt. You can calculate phase noise by applying the Fourier transform to V_OUT(t), but the result is difficult to solve analytically. As an approximation³, the phase noise is

where Sφ is the spectral density of φ(t) and S_V(ƒ_n) is the spectral density of V_n(t) in V²/Hz. The phase-noise profile, therefore, takes the same shape as the modulating noise-density profile. For a white-noise source followed by a 100 kHz lowpass filter, the phase-noise profile is the same as the filter's frequency response. In that case, the phase-noise level is constant inside the filter's cut-off frequency and rolls off outside the -3 dB bandwidth (Figure 3). This phase-modulator circuit provides a convenient way to produce a variable phase-noise signal that mimics real world noisy signal sources — such as phase-locked oscillators.

The circuit of Figure 1b works well from 5 MHz to 30 MHz, and you can easily scale the inductor and capacitor values for operation at other frequencies. Lab experiments show that the circuit can be scaled up to 2 GHz or 3 GHz. Those frequencies require about 1 nH inductance and 1 pF capacitance, so the technique is frequency-limited by component availability and PCB parasitics.

A change in the varactor capacitance changes the noise-signal amplitude as well as phase, but amplitude changes are much smaller than the phase changes. The phase changes represent phase noise, and the amplitude changes represent amplitude noise (Figure 4). This modulator produces about 30 dB greater phase modulation than amplitude modulation, thereby ensuring that the phase noise is dominant.

Many methods are available for generating noise voltage for the phase-noise modulation. The simplest way is to reverse-bias a zener diode in its avalanche-breakdown region (Figure 5a). The diode's excess shot noise is amplified by both the fixed-gain and the variable-gain amplifiers. The gain of these cascaded amplifiers must be high enough to produce the desired noise voltage level. The noise output is followed by a filter that shapes the noise according to the phase-noise profile required in Figure 1a or 1b. (An advantage of the 1b circuit is that the shape of the noise-source profile is the same as the output phase-noise profile.)

The phase-noise profile of an actual oscillator can be complicated. It might roll off at 30 dB/decade for low offset frequencies, become flat inside the loop bandwidth, roll off 20 dB/decade outside the loop bandwidth, and finally assume a flat noise floor (Figure 6). In addition, there may be a few sets of reference spurs.

Such phase-noise profiles require a more complicated noise-generation circuit like the one shown in Figure 5b. It produces complicated, multisegment noise profiles using a microprocessor or digital signal processor (DSP) and a digital-to-analog converter (DAC). For the phase modulator of Figure 1b, a flat phase-noise region is produced by a white Gaussian-noise voltage followed by a digital filter with flat frequency response in the offset frequency of interest (i.e., a bandpass filter). To produce the required roll-off slope, a white Gaussian noise is followed by a finite impulse response (FIR) or infinite impulse response (IIR) digital-filter algorithm. For spurs, you can add a sinusoid to the noise voltage. Then, sum all of these noise segments together. Still in digital format, the noise voltage is converted to an analog voltage by the DAC, followed by a reconstruction filter.

The techniques for producing phase noise are illustrated in Figure 1, and the techniques for producing noise voltage are illustrated in Figure 5. The Figure 1a circuit produces phase noise by modulating the VCO tuning input directly, and the Figure 1b circuit generates phase noise with an external phase modulator. Each technique produces a different phase-noise profile. The direct modulation technique of Figure 1a works at any VCO frequency. For the phase-modulator technique of Figure 1b, the carrier frequency is limited to a few gigahertz by component availability and PC-board parasitics.

1. Behzad Razavi, RF Microelectronics. Upper Saddle River, NJ, 1998, p. 223.

2. Enrico Rubiola et. al., “The ±45° Correlation Interferometer as a Means to Measure Phase Noise of Parametric Origin,” IEEE Transactions On Instrumentation and Measurement, Vol. 52, No. 1, pp. 182-188.

3. A.L. Lance et. al., “Phase Noise Measurement Systems,” ISA Transactions, Vol. 21, No. 4, pp. 37-44.

Ken Yang is a supervisor and senior member of the technical staff at Maxim Integrated Products. He received a B.S. degree in physics from Washington State University and an MSEE from the University of California, San Diego.