vco design using spectrerf application note -...

VCO Design Using SpectreRFApplication Note

Product Version 5.0December 2003September 2004

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VCO Design Using SpectreRF

Contents

Voltage Controlled Oscillator Design Measurements . . . . . . . . . 5

Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Audience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Introduction to VCOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5VCO Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Output Frequency and Output Power Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Frequency Pushing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Frequency Pulling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Tuning Sensitivity and Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Power Dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Example VCO Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Example VCO Schematic: oscHartley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Output Frequency and Output Power Level (PSS) . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Phase Noise (PSS and Swept Pnoise) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Frequency Pushing (Swept PSS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Frequency Pulling (Swept PSS on Modified Hartley Schematic) . . . . . . . . . . . . . . . . 23Tuning Sensitivity and Linearity (Swept PSS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Power Dissipation (PSS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

September 2004 3 Product Version 5.0


Voltage Controlled Oscillator DesignMeasurements

The procedures described in this application note are deliberately broad and generic. Yourspecific design might require procedures that are slightly different from those described here.

Purpose

This application note describes how to use SpectreRF in the Analog Design Environment tomeasure parameters which are important in design verification of voltage controlledoscillators, or VCOs.

Audience

Users of SpectreRF in the Analog Design Environment.

Overview

This application note describes a basic set of the most useful measurements for VCOs.

Introduction to VCOs

Oscillators generate a reference signal at a particular frequency. In voltage controlledoscillators, or VCOs, the frequency of the output varies in proportion to some control signal.Oscillators are generally used in RF circuits to generate the local oscillator, or LO, signal formixers. VCOs are used in both receivers, as shown in Figure 1-1, and transmitters, as shownin Figure 1-2.


VCO Design Using SpectreRFVoltage Controlled Oscillator Design Measurements

Figure 1-1 Block Diagram of a Typical Superheterodyne Receiver

The noise performance of a mixer is strongly affected by noise on the LO signal. The LOsignal is always passed through a limiter, which is generally built into the mixer, to make themixer less sensitive to small variations in the amplitude of the LO signal. In addition, alloscillators, except the reference oscillator, are embedded in phase-locked loops to controltheir frequency and reduce their phase noise. (Reference oscillators are generally fixed-frequency crystal oscillators, and as such have well controlled frequency and noise.)

However, oscillators still produce enough variation in the phase of their output to affect theperformance of the tranceiver. Thus, it is important to minimize the phase noise produced bythe oscillator.

Figure 1-2 RF Interface for A Digital Direct Conversion Transmitter



Nonlinear oscillators naturally produce high levels of phase noise. To see why, consider thetrajectory of an oscillator’s stable periodic orbit in state space. Furthermore, considerdisturbing the oscillator by applying an impulse u(t) = δ(t). The oscillator responds by followinga perturbed trajectory x(t) + ∆x(t) as shown in Figure 1-3, where

■ x (t) represents the unperturbed solution

■ ∆x (t) is the perturbation in the response.

Figure 1-3 Oscillator Trajectory in State Space With and Without Perturbation ∆x

Figure 1-3 shows the trajectory of an oscillator shown in state space with and without aperturbation ∆x. By observing the time stamps (t0,..., t6) you can see that the deviation inamplitude dissipates while the deviation in phase does not.

Equation 1-1 shows the decomposition of the perturbed response into amplitude and phasevariations.

where

■ v (t) represents the noisy output voltage of the oscillator

■ α (t) represents the variation in amplitude

■ φ (t) is the variation in phase

■ f0 is the oscillation frequency

(1-1) v t( ) x t( ) ∆x t( )+ 1 α t( )+( )x tφ t( )

2πf 0-------------+

= =



Since the oscillator is stable and the duration of the disturbance is finite, the deviation inamplitude eventually decays away and the oscillator returns to its stable orbit. In effect, thereis a restoring force that tends to act against amplitude noise. This restoring force is a naturalconsequence of the nonlinear nature of the oscillator and at least partially suppressesamplitude variations, as shown in Figure 1-4. With linear oscillators, there is no restoring forceand so the amplitude is arbitrary (that is, they do not have stable orbits). As such, linearoscillators exhibit equal amounts of amplitude and phase noise because the amplitude noiseis not suppressed.

Figure 1-4 Linear Oscillator (left) and Nonlinear Oscillator (right) Each With ItsResponse to Noise

Figure 1-4 shows

■ On the left, a linear oscillator and its response to noise.

■ On the right, a nonlinear oscillator and its response to noise.

In Figure 1-4, the arrows are phasors that represents the unperturbed oscillator output, thecarriers, while the circles represent the response to perturbations in the form of noise. For thelinear oscillator on the left, the noise simply adds to the carrier. For the nonlinear oscillator onthe right, the nonlinearities act to control the amplitude of the oscillator and so to suppressvariations in amplitude, thereby radially compressing the noise ball and converting it intopredominantly a variation in phase.

Since an oscillator is autonomous, any time-shifted version of the solution is also a solution.Once the phase has shifted due to a perturbation, the oscillator continues on as if neverdisturbed except for the shift in the phase of the oscillation. There is no restoring force on thephase and so phase deviations accumulate. This is true for both linear and nonlinearoscillators. Notice that there is only one degree of freedom — the phase of the oscillator asa whole. There is no restoring force when the phase of all signals associated with theoscillator shift together, however there would be a restoring force if the phase of signalsshifted relative to each other. This is important in oscillators with multiple outputs, such asquadrature oscillators or ring oscillators. The dominant phase variations appear identically in



all outputs, whereas relative phase variations between the outputs are naturally suppressedby the oscillator or added by subsequent circuitry and so tend to be much smaller.

After being disturbed by an impulse, the asymptotic response of the amplitude deviation isα (t) → 0 as t → ∞. However, the asymptotic response of the phase deviation is φ ( t) → ∆φ. Ifresponses that decay away are neglected then the impulse response of the phase deviationφ (t) can be approximated with a unit step s (t). Thus, Equation 1-2 shows the phase shift overtime for an arbitrary input disturbance u.

Equation 1-3 shows the power spectral density (PSD) of the phase.

The disturbance u might be either deterministic or random in character. It might result fromextraneous signals coupling into the oscillator or from variations in the components that makeup the oscillator, such as thermal, shot, and flicker noise.

If Su ( f ) is white noise, then Sφ( f ) is proportional to 1 / (2πf )2. This result has been shownhere to apply at low frequencies, but with a more detailed derivation the result can also beshown to be true over a broad range of frequencies. Assume u is white and define a such that

where f0 = 1 / T is the oscillation or carrier frequency. Sφ is the PSD of the phase variable inEquation 1-1 on page 7. Phase cannot easily be observed directly, so instead you are ofteninterested in Sv, the PSD of v. near the fundamental [1].

(1-2)

(1-3)

(1-4)

φ t( ) s t τ–( )u τ( ) τd

∞–

∞

∫∼ u τ( ) τd

∞–

t

∫=

Sφ f( )Su f( )

2πf( )2-----------------∼

Sφ f( ) af 0

2

f 2-------=



where fm is the frequency offset from the fundamental and X1 is the first Fourier coefficient forx,

This spectrum is a Lorentzian as shown in Figure 1-5. The corner frequency f∆ is known asthe linewidth of the oscillator and is given by f∆ = aπf0

2, with

Figure 1-5 Different Ways to Characterize Noise in the Same Oscillator

Figure 1-5 shows two different ways of characterizing noise in the same oscillator. Sφ is thespectral density of the phase and Sv is the spectral density of the voltage. Sv contains bothamplitude and phase noise components, but with oscillators the phase noise dominatesexcept at frequencies far from the carrier and its harmonics. Sv is directly observable on aspectrum analyzer, whereas Sφ is only observable if the signal is first passed through a phasedetector. Another measure of oscillator noise is L, which is simply Sv normalized to the powerin the fundamental.

Sv f 0 f m+( ) X12

a f 02

a2π2 f 04 f m

2+-----------------------------------=

x t( ) Xkej2πk f 0t

k ∞–=

∞∑=

Sv f 0 f m+( )X1

2

π-------------

f ∆f ∆

2 f m2+

----------------------=



As t → ∞ the phase of the oscillator drifts without bound, and so Sφ(fm) → ∞ as fm → 0.However, even as the phase drifts without bound, the excursion in the voltage is limited by thediameter of the limit cycle of the oscillator (represented by the periodic function x inEquation 1-1 on page 7). Therefore, as fm → 0 the PSD of v flattens out and

which is inversely proportional to a. Thus, the larger a, the more phase noise, the broader thelinewidth, and the lower signal amplitude within the linewidth. This happens because thephase noise does not affect the total power in the signal, it only affects its distribution. Withoutphase noise, Sv (f) is a series of impulse functions at the harmonics of f0. With phase noise,the impulse functions spread, becoming fatter and shorter but retaining the same total power.

It is more common to report oscillator phase noise as L, the ratio of the single-sideband (SSB)phase noise power to the power in the fundamental (in dBc/Hz)

At frequencies where the oscillator phase noise dominates over the amplitude noise, and thatare also outside the linewidth (fm > f∆), the phase noise is approximated with

Other references report that L (fm) = Sφ(fm) / 2, which is true when Sφ is the single-sided PSD[1]. Here Sφ is the doubled-sided PSD.

The roll-off in Sv (f0 + fm) and L (fm) as fm → 0 is a result of the circuit responding in a nonlinearfashion to the noise itself. As such, it cannot be anticipated by the small-signal noiseanalyses. However, as you can see from Figure 1-5, Sφ does not roll-off at low frequencies,so you can use these analyses along with Equation 1-6 to compute Sφ at low frequencies.

(1-5)

(1-6)

Sv f 0 f m+( )X1

2

πf ∆-------------→

L f m( )Sv f 0 f m+( )

X12

--------------------------------1π---

f ∆f ∆

2 f m2+

----------------------= =

L f m( )f ∆

π f m2

------------a f 0

2

f m2

---------- Sφ f m( ) for f ∆ f f 0« «= = =



When the perturbation consists of the white and flicker noise, the phase-noise Sφ(fm) will takethe form shown in Equation 1-7 [1].

Thus, you can characterize the oscillator’s response to white and flicker noise sources usingjust two parameters, af0

2 and fc, where

■ af02 is the portion of the phase-noise attributable to the white noise sources alone at

fm = 1 Hz. You can extract this by simply extrapolating to 1 Hz from a frequency wherethe noise from the white noise sources dominates.

■ fc is the flicker noise corner frequency, where white noise and flicker noise have the samecontribution to phase noise.

Figure 1-6 shows an oscillator phase noise curve.

Figure 1-6 Typical Phase Noise Curve for an Oscillator

SpectreRF uses the following general procedure to measure oscillator noise.

1. Perform a periodic steady state (PSS) analysis.

2. Use the measured periodic steady state as the operation point to obtain the linearperiodic time varying (LPTV) model.

(1-7) Sφ f m( ) a f 02 1

f m2

-------f c

f m3

-------+

=



3. Calculate the total voltage noise contribution at the output from every noise source usingthe LPTV model.

4. Scale the voltage-noise spectrum by the power of the fundamental to obtain the phasenoise spectrum using Equation 1-6.

Because an oscillator LPTV model has a singularity pole at f0, the oscillation frequency, thetotal output noise calculated using the LPTV model approaches infinity as fm → 0. However,this is not physically correct because the nonlinearity of the oscillator limits the voltageamplitude and the LPTV model ignores the nonlinearity effect. Therefore, the correct Sv( f )curve should be flat in the vicinity of f0.

Although the amplitude of the voltage at the output is bounded due to the nonlinearity effect,the phase of the voltage is not bounded. So the phase noise grows as the offset frequencyfm → 0. Physically this means that if the frequency of the perturbation to the oscillator is thesame as its oscillation frequency, the phase of the output voltage will accumulate and growwithout bound.

Since the voltage noise calculated from the LPTV model also grows as the offset frequencyapproaches 0, the phase noise calculated by the voltage noise from the LPTV model is stillcorrect using Equation 1-6 for small offset frequency.

Now the question becomes how to get the real Sv( f ) from the calculated Sv( f ) using the LPTVmodel. In other words, you must estimate the linewidth where Sv( f ) is becoming flat. Withoutthe flicker noise, the linewidth is

and you can obtain af02 from the extrapolated Sφ at 1 Hz due to white noise. Calculate the

linewidth by integrating L( fm ) over fm and set the result equal to 0.

When both white noise and flicker noise exist, you can use a similar technique to obtain theapproximate linewidth as in Equation 1-8.

Phase noise acts to vary the period of the oscillation, a phenomenon known as jitter. Onejitter metric is k-period jitter, which is defined as the time for k periods, as shown in Equation1-9.

(1-8)

f ∆ aπf2

0=

a2

f4

0af

2

0f c+ π 1–( )af

2

0+



Consider the relationship between the phase and k-period jitter as shown in Equation 1-10,

The variance of the k-period jitter and phase-noise are related as shown in Equation 1-11 [2].

When you substitute the Sφ from Equation 1-7 on page 12 into Equation 1-11 and ignore theflicker noise part, the k-period jitter is defined as in Equation 1-12.

Obtain the parameter a by extrapolating Sφ at 1 Hz due to white noise. When the flicker noisepart exists in phase noise, the integration in Equation 1-11 is not bounded. It shows that thevalue of k-period jitter is undefined when there is any flicker noise component in the oscillatorphase noise because the result is dependent on how long the jitter is observed and how manysamples the measurement takes.

VCO Measurements

To achieve optimal circuit performance, you should measure and evaluate several VCOcharacteristics or parameters under varying conditions. As an example, one fundamentalparameter is the plot of VCO output frequency versus tuning voltage. An extension of thisparameter is tuning sensitivity (expressed in Hz/V), which is the differential of the outputfrequency versus tuning voltage curve. The slope change as a function of frequency is ofparamount importance since this is a critical design parameter.

(1-9)

(1-10)

(1-11)

(1-12)

Jk tn k+ tn– kT–={ }

Jk

φ tn k+( ) φ tn( )– 2πk–( )

2πf--------------------------------------------------------------=

Jk2 2T 2

π2---------- Sφ f( ) πfkT( )sin2 fd

0∞∫=

Jk2 akT=



In practice, both of these parameters should be evaluated under different supply (Vcc)conditions since the output frequency may shift with Vcc changes. This DC power sensitivityis called frequency pushing.

The RF power output is also a function of both Vcc and output frequency. You should evaluatethe RF power output since an output power level that is too low results in excessive noise andan output power level that is too high creates distortion and consumes excess DC power.Moreover, the DC power has the chance to translate Vcc noise into oscillator outputmodulation and noise.

There are many parameters you must evaluate that are not covered in this application note.The parameters that are covered in this application note are listed and described in thefollowing sections.

Output Frequency and Output Power Level

Usually you cannot specify an analysis period for an autonomous circuit because you do notknow the precise oscillation period in advance. To that end, you can estimate the oscillationperiod and SpectreRF will compute the correct period. The output power of a VCO is typicallyexpressed in dBm.

Phase Noise

Phase noise is random phase variation in the VCO’s output oscillating signal. Close to thecarrier phase noise is mainly composed of flicker noise. The flicker noise measured in a VCOis generated only by the active devices, such as the transistor and the tuning diode. Thephase noise is measured at distances from 1 KHz off the carrier to several megahertz (MHz)off the carrier in a 1-Hz bandwidth. Phase noise is the ratio of the output power divided by thenoise power at a specified value and is expressed in dBc/Hz. Phase noise is the mostsignificant source of noise in oscillators, which makes it a crucial measurement.

Frequency Pushing

Frequency pushing is the variation of the VCO output frequency due to a change in thepower supply (Vcc). One way to measure frequency pushing is as follows.

1. Set the supply voltage (Vcc) at its nominal setting and compute the VCO frequency fordifferent tune voltages.

2. Increase the supply voltage by a specific amount, ∆v, and measure the VCO frequencyfor different tune voltages as before.



3. Decrease the supply voltage by the same amount, ∆v, from the nominal value, andmeasure the frequency for different tune voltages as before.

At a given tuning voltage, the frequency change due to a 1 volt supply voltage change yieldsthe frequency pushing. Frequency pushing may be different at different tuning voltages.

Frequency Pulling

Frequency pulling is a measure of frequency change due to a non-ideal load. You measurefrequency pulling by noting the frequency change caused by a load having a nominal 12 dBreturn loss with all possible phases. You should minimize frequency pulling, especially incases where power stages are close to the VCO unit and short pulses might affect the outputfrequency.

Tuning Sensitivity and Linearity

Tuning sensitivity is defined as the frequency change per unit of tuning voltage. Ideallytuning sensitivity would be constant but in practice this is generally not the case.

1. Compute the VCO frequency for different tuning voltages.

2. Plot VCO frequency measurements against tuning voltage. The slope of thischaracteristic is the tuning voltage sensitivity which you can calculate at different tuningvoltages.

The tuning sensitivity is expressed in Hz/V.

Power Dissipation

Power Dissipation arises from the following sources:

■ Dynamic power dissipation due to switching current from charging and dischargingparasitic capacitance.

■ Dynamic power dissipation due to short-circuit current when both n-channel andp-channel transistors are momentarily on at the same time.

■ Static power dissipation due to leakage current and subthreshold current.

VCOs suffer from trade-offs between speed, power dissipation, and noise. Typically, theydrain from 1 to megawatts, mW, of power.



Example VCO Measurements

The VCO measurements in the following sections are calculated using SpectreRF version 5.0in the analog design environment.

Example VCO Schematic: oscHartley

Note: In Version 5.1.41 USR1 and later, you will find the oscHartley VCO schematic in therfExamples library which is available with the Virtuoso® SpectreRF Simulator Option.

The oscHartley oscillator circuit that was chosen to conduct the measurements described in“VCO Measurements” on page 14 is shown in Figure 1-7 on page 18. The oscHartley VCOuses the basic Hartley topology and is tunable between 720 MHz and 1.1 GHz. Theoscillation frequency (Fo) is determined by the resonant circuit made up of inductors (L0, L1)and the C1 capacitor. In this particular VCO, the values of L1 and L2 are fixed whereas thevalue of C1 is variable.

In this example, the resonant circuit’s capacitor C1 serves as a varactor diode. As a result, thevaractor diode’s junction capacitance, Cvar, is a function of the applied voltage as shown inequation 1-13.

Where

■ V = applied junction voltage (V)

■ Cj0 = junction capacitance (F) for V = 0 V

■ φ = barrier potential (V)

■ ϒ= junction gradient coefficient

The varactor diode for this VCO has the following values

■ Cj0 = 8 pF

■ φ = 0.75 V

■ ϒ= 0.4

(1-13) CvarC j0

1 Vφ----+

-------------------

ϒ=



Because Cvar is inversely proportional to V, and Fo is inversely proportional to Cvar, theoscillation frequency is proportional to V. In other words, as you increase V, Cvar decreasesand Fo increases.

Figure 1-7 The Hartley Oscillator

Output Frequency and Output Power Level (PSS)

Testbench:

Hartley Oscillator in Figure 1-7.



Initial Conditions/Kickstart:

Pulse source.

Set Up the Analysis:

Set up a PSS analysis with

■ Beat Frequency = 600 M

■ Number of Harmonics = 3

■ errpreset = moderate

■ tstab = 120 n

■ Enable the oscillator button

■ Set Oscillator node = /Vout

■ Set Reference node = /gnd!

Run the Simulation:

Before you run the PSS analysis, to obtain the Output Power Level at the load, you must savecurrent at the /Vout net through the Analog Design Environment. The Outputs section ofthe Analog Design Environment window must display, /Vout with the Save column set toyes.

Run the PSS analysis.

Display/Data Analysis:

SpectreRF outputs a Fundamental Frequency = 1.1149 GHz in the Spectre log file.

Select Results--Direct Plot--Main Form; press on the Power button; select Net (specifyR) and set Resistance = 10 K; press the dBm button; and finally select the /Vout net onthe schematic. The plot in Figure 1-8 is displayed.



Figure 1-8 Output Frequency and Output Power Level Plot

Phase Noise (PSS and Swept Pnoise)

Testbench:

Hartley Oscillator in Figure 1-7 on page 18.


Pulse source.

Set Up the Analyses:

Set up a PSS analysis and a Swept Pnoise analysis.

■ Set up a PSS analysis with a Beat Frequency = 600 M; Number of Harmonics = 3;errpreset = moderate; tstab = 120 n; enable the oscillator button; setOscillator node = /Vout; and Reference node = /gnd!.

■ Set up a swept Pnoise analysis with a Sweeptype = relative; Relative Harmonic = 1;Frequency Sweep Range (Start = 1 K, Stop = 10 M); set Sweeptype = logarithmic; Number of Steps = 100; Maximum sideband = 15; set



Output = voltage; Positive Outtput Node = /Vout!; Negative Output Node = /gnd!, and Input Source = none.

Run the Simulation:

Run the PSS and swept Pnoise analyses.


Click Results--Direct Plot--Main Form; enable the pnoise button; click on the PhaseNoise button; and finally click on Plot. The plot in Figure 1-9 will be displayed.

Figure 1-9 Phase Noise Plot

Frequency Pushing (Swept PSS)

Testbench:

Hartley Oscillator in Figure 1-7 on page 18.




Pulse source.


Calculate frequency pushing with a swept PSS analysis. Parametrize the Vcc supply variableand run a swept PSS analysis for different values of the Vcc parameter. To do this, edit theobject properties of the vpulse source cellname, and change the value of voltage 2 from5 V to fvcc V, then select Check and Save for the schematic.

Set up a swept PSS analysis with a Beat Frequency = 1.115 G; Number ofHarmonics = 3; errpreset = moderate; tstab = 120 n; enable the oscillator button; setOscillator node = /Vout; and Reference node = /gnd!; enable the Sweep button; enterfvcc as Variable Name; set the Sweep Range Start = 4 and Stop = 6; set SweepType = linear; and Number of Steps = 10.

Run the Simulation:

Run the swept PSS analysis.


Click Results--Direct Plot--Main Form; click on the Harmonic Frequency button,highlight the 1-st harmonic in the Harmonic Frequency section; and press on the plotbutton. The plot in Figure 1-10 is displayed.



Figure 1-10 Frequency Pushing

Frequency Pulling (Swept PSS on Modified Hartley Schematic)

Make frequency pull calculations on a Modified copy of the Hartley Oscillator shown inFigure 1-7 on page 18.

Testbench:

Modify the Hartley Oscillator shown in Figure 1-7 on page 18 for frequency pull calculations.

➤ Copy the Hartley schematic and modify the copy as follows

a. Connect an instance of a PortAdaptor to the load.

b. Select the PortAdaptor you just added, choose Edit-Properties-Objects, enterthe following data and click Apply:

❍ Frequency = 1.115 G;

❍ Phase of Gamma = theta;



❍ Mag of Gamma = 0.2512

❍ Reference Resistance = 10K (this value must equal the load).

Note: To find out how to place an instance of a PortAdaptor in a schematic, read thetransmitter modeling chapter in the SpectreRF User’s Guide.

Frequency pulling is the measurement of frequency change caused by a load having anominal 12 dB return loss with all possible phases. The value of Mag of Gamma, 0.2512,is computed from the return loss value, rl, using the following formula:

where Γ is the reflection coefficient with respect to a source impedance R0.

The modified Hartley oscillator used to calculate frequency pulling is displayed in Figure 1-11.

rl 20Log Γ–=



Figure 1-11 Hartley Oscillator Modified for Frequency Pull Measurements


Pulse source.


Calculate frequency pulling with a swept PSS analysis. Set up a swept PSS analysis with thethe theta parameter varying from 0 to 359 degrees.

Set up a swept PSS analysis with Beat Frequency = 1.115G; Number of Harmonics = 3;errpreset = moderate; tstab = 120n; enable the oscillator button; set Oscillator node = /



Vout; and Reference node = /gnd!; enable the Sweep button; enter theta as VariableName; set the Sweep Range Start = 0 and Stop = 359; set Sweep Type = linear; andNumber of Steps = 10.

Run the Simulation:



Click Results--Direct Plot--Main form; click on the Harmonic Frequency button; highlightthe 1-st harmonic in the Harmonic Frequency section; and press on the Plot button. Theplot in Figure 1-12 is displayed.

Figure 1-12 Frequency Pulling

The peak to peak difference in the displayed frequency in Figure 1-12 gives the load pull.



Tuning Sensitivity and Linearity (Swept PSS)

Testbench:

The original, unmodified Hartley Oscillator shown in Figure 1-7 on page 18.


Pulse source.


Run a swept PSS analysis with a Beat Frequency = 1.115G; Number of Harmonics = 3,errpreset = moderate, tstab = 120n. Enable the oscillator button, set Oscillator node = /Vout, and Reference node = /gnd!. Enable the Sweep button, enter V_cntl as VariableName (this is the tuning voltage), set the Sweep Range Start = 0 and Stop = 6, set SweepType = linear, and Number of Steps = 6.

Run the Simulation:



Click Results--Direct Plot--Main form, click on the Harmonic Frequency button, highlightthe 1-st harmonic in the Harmonic Frequency section and press the Plot button. The plotin Figure 1-13 is displayed.



Figure 1-13 Frequency Change per Unit Volt of Tuning Voltage

Figure 1-13 represents the frequency change per unit volt of tuning voltage.



Figure 1-14 Tuning Voltage Sensitivity

Figure 1-14 represents the tuning voltage sensitivity. Use the Calculator function in theAnolog Design Environment to create this plot.

Power Dissipation (PSS)

Testbench:

The original, unmodified Hartley Oscillator shown in Figure 1-7 on page 18.


Pulse source.


Set up a PSS analysis with a Beat Frequency = 1.115G; Number of Harmonics = 3;errpreset = moderate; tstab = 120n; enable the oscillator button; set Oscillator node = /Vout; and Reference node = /gnd!.



Run the Simulation:

Run the PSS analysis.

To obtain the Power Dissipation, before you run the PSS analysis, you must save data at theVcc terminal through the analog design environment. The Outputs section of the analogdesign environment window must display, p(/V0/PLUS /vcc!) with the Save column setto yes.


Click Results--Direct Plot--Main form. Highlight the Power button, select Terminal,highlight the dB10 button. In the schematic, select the V0/PLUS terminal of the Vcc powersupply and press the Plot button. The plot in Figure 1-15 is displayed.

Figure 1-15 Power Dissipation

Power dissipation is the value that corresponds to the DC value in Figure 1-15; that is, atfreq = 0.0 the power dissipation value is equal to -16.81 dB or 13.19 dBm.



Conclusions

This application note describes some of the most useful measurements for VCOs. SpectreRFmeasurements such as Frequency Pushing, Frequency Pulling, Tuning Sensitivity, PowerDissipation, and Linearity are discussed.

References

[1] Ken Kundert, “Introduction to RF Simulation and Its Application”, www.designers-guide.com

[2] Ken Kundert, “Predicting the Phase Noise and Jitter of PLL-Based FrequencySynthesizers”, www.designers-guide.com

[3] Ken Kundert, Manolis Terrovitis, “Converting Phase-Noise to Jitter”, Cadence report.


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