measuring non-linear amplifiers - aalborg...

Jan Hvolgaard Mikkelsen

Radio Frequency Integrated Systems and Circuits DivisionAalborg University

2007

Measuring Non-linear AmplifiersTransceiver Components & Measuring Techniques

MM3

Jan Mikkelsen -2-

Agenda

• Non-linear measurement

Signal combining· Hybrids

· Circulators

• The spectrum analyzer

Resolution Bandwidth/Phase noise

Internally Generated Distortion

Video Filter

Filter selectivity

Input attenuation

Dynamic Range / Dynamic Range Graph

• Digital Spectrum Analyzers

Differences

Advantages/Disadvantages

• Power measurement

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How is IPn measured?

• Depending of the type of IPn measurement different combinations of input signals are required.

• The IPn performance of a specific device may be measured in different ways and using different input signal conditions.

• Remember to measure the device using the same input conditions as used for the receiver or transmitter planning.

Single-tone versus modulated single-tone versus two-tone.

• Signal generators may be used to supply two sine-waves of equal amplitude but different frequencies.

• The resulting output spectrum may be measured using a spectrum analyzer.

DUTSpectrum Analyzer

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Signal generator non-idealities

• Just as our ”linear” amplifier proves to be non-linear when tested, signal generators also display non-ideal behavior.

• Signal generators are active circuits.

The generated signal contains harmonics.

A certain frequency error (usually small for SOA generators).

Phase noise from the Local Oscillator.

• If the isolation between two distinct generators is too low the generators will also generate intermodulation products in addition to signal harmonics (as well as source pulling etc.).

• Combining circuits must be utilized to provide for adequate isolation.

Attenuators.

Circulators / Isolators.

Hybrids.

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Combining / Signal Isolation

• Circulators or isolators useferromagnetic materials to providenon-reciprocal signal transmission.

• Hybrids combine paths withdifferent electric lengths in a waythat the output is a combination ofthe input signals while isolating thetwo input ports.

90 degree hybrids (Quadrature).

180 degree hybrids.

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

010001100

CS

1

3

2

1 2

34

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−−=

0110100110010110

2j

HS

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡−−

=

010001

100010

21

jj

jj

HS

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Combining/Signal Isolation

• Non-50Ω impedances at the DUT input affect performance of bothhybrids and circulators/isolators.

• Even for a perfect hybrid, non-50Ω impedances have an impact as seenfrom the resulting S-matrix.

0

0L ;

111001101

11

2 ZZZZj

L

L

LL

L

LL

H +−

=Γ

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

Γ−Γ

−Γ−Γ−Γ

−=S

50 Ω

50 Ω

ZL

50 Ω

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−−=

0110100110010110

2j

HS

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Combining/Signal Isolation

• Non-50Ω impedances at the DUT input affect performance of bothhybrids and circulators/isolators.

• For a perfect circulator the S-matrix now becomes:

0

0L ;

01001

10

ZZZZ

L

LL

L

C +−

=Γ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡Γ

Γ−=S

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

010001100

CS

50 Ω

ZL

50 Ω

• Now that some of the important details for the input side is understood it is time to consider the output also.

• Only once the test set-up is fully know is it possible to ensure optimum settings for any given DUT.

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What is inside a spectrum analyzer?

Pre‐selectInput attn. Mixer

IF‐ampIF‐filter Detector

VideoFilter

DisplayRamp

GeneratorReference XO

VCO

• The analyzer relocates the input to lower frequency where it estimatesthe resulting power.

• A ramp sweeping LO is used to evaluate different frequencies and plot the power at these.

x-axisx-axis

y-axisy-axis

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What is inside a spectrum analyzer? - II

• To achieve a high frequency resolution very sharp filters are needed.

• Some analyzers have resolutions in the order of 10-100Hz .. and such a level of resolution is NOT achieved at 6GHz.

• Instead several mixer stages are used to down convert the input signal to more manageable frequencies.

x-axisx-axis

y-axisy-axis

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Limitations of the spectrum analyzer

• The spectrum analyzer (SA) is in principle an RF receiver and as such it adds both noise and distortion to the input signal.

• The SA also has a finite selectivity which also affect performance.

• Such non-ideal effects set a limit on a number of important parameters.

Signal frequency spacing.

Minimum/Maximum input power (Dynamic Range).

Maximum amplitude difference.

• Spectrum analyzers can be adjusted in a variety of ways which provides a trade-off situation.

• Measurement sweep time is traded for resolution and the same goes for the noise.

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SA limitations – frequency resolution

• Consider the case where a single-tone input signal signal is being feed to the SA.

• As the LO changes in frequency so vil the mixing product of the input signal.

• Due to the finite band width of the IF filter output power is going to be detected at a frequency range around the ”input frequency”.

• As a result the characteristics of the IF filter is reflected on the display of the SA.

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SA limitations – frequency resolution - II

• The IF filter with the lowest bandwidth consequently sets the limitation on the achievable frequency resolution.

• The finite IF filter bandwidth ”smears” the signal across a frequency band and could eventually case signals to ”disappear”.

• Noise floor and LO phase noise set a limit to the amplitude sensitivity.

Noise FloorPhase noise

IF filter BW

Noise FloorPhase noise

if we arelucky ..

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SA limitations – frequency resolution - III

• For equal-amplitude signals requirements are not to strict .. but for different amplitudes the resolution is extremely important.

• Resolution bandwidth (RBW) is the user parameter that determines the frequency resolution of the SA.

• By changing the RBW setting it is possible to change the IF bandwidth of the SA.

• Not only does this affect the ”frequency masking” performance it also affects the noise floor level of the SA.

RBW too high

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SA limitations – frequency resolution - IV

• When working with signals of different amplitudes we need to determine what RBW is allowable.

• To characterize the different RBW settings a term called bandwidth selectivity (or shape factor) is used.

• Shape factor is the ratio between the 3dB bandwidth and the 60dB bandwidth.

• For analog filters a shape factor of 1:15 is typical.

• For digital filters much sharper filters are possible and typical shape factors are around 1:5.

• When trying to determine the allowable RBW we need to know the shape factor of the band limiting IF filter.

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SA limitations – frequency resolution - V

• Using the example from the Agilent application note .. what RBW is required to resolve two signals with a 4kHz offset in frequency and a 30dB offset in amplitude assuming a shape factor of 1:11?

4kHz

30dB

• With amplitude (power) in a log scale we assume that there is a linear relation between the 3dB and the 60dB frequencies of the IF filter.

• We may hence determine the attenuation of the filter at the given offset using the following formula:

dBdBdBdB

dBoffset

offset DIFFBWBW

BWfdBATT 603

360

3

22

23 >−⋅−

−−−=

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SA limitations – frequency resolution - VI

• Using a 3kHz filter as a first guess we can calculate the attenuation as follows:

dBdBkHzkHz

kHzkHzdBATT kHz 5.1257

23

233

234

34 −=⋅−

−−−=

dBdBkHzkHz

kHzkHzdBATT kHz 9.4257

21

211

214

34 −=⋅−

−−−=

• This is clearly not sufficient to resolve a 30dB difference and we need to go for a lower RBW .. 1kHz for instance:

• According to this a 1kHz RBW is sufficient when we want to resolve a 30dB difference at the 4kHz offset.

• As an example lets assume an actual 0dBm input signal:

dBmWmWPPP leakactualMeas 22.02.511 =+=+= μ

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SA limitations – frequency resolution - VII

• When illustrated graphically the effect of the two RBW settings (3kHz and 1kHz) becomes very clear.

1kHz

3kHz

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Digital Spectrum Analyzers

• Clearly, the shape factor has a major impact on the resolution performance of the analyzer.

• This is partly why most modern analyzers use digital LF/basebandprocessing .. remember the typical shape factor of 1:5 .

• The block diagram of a digital SA does not differ significantly from the block diagram for an analog analyzer shown earlier .

Pre‐selectInput attn. Mixer

IF‐ampIF‐filter

IF ADC

OCXO

Frq. Synth DSP

CRT DisplayEthernetGPIBHarddisk

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• The down-converted input signal is normally sampled at IF signal and subsequently I/Q down-converted in the digital domain.

A clear benefit from this is that ”perfect” I/Q balance results.

• If the analyzer uses both I and Q branches for its signal processing it is referred to as a Vector Signal Analyzer (VSA).

• VSAs can analyze the signal using both amplitude and phase which is especially interesting when doing modulation measurements.

NCO

0°

90°

Filter Coefficients

I(n)

Q(n)

22 )()()( nQnInA +=

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• There are a number of good reasons that speak in favor of the digital analyzers.

• Going from analog to digital means better control over many aspects of the detection.

Phase information can be extracted.

Filters can be controlled much more efficiently.

DSPs can control many of the spectrum analyzer’s internal functions (such as input attenuation).

• There is however one very important effect to consider for digital spectrum analyzers that is not seen in their analog counterparts.

• Instead of using a continuous ramp signal (analog) the local oscillator is stepped over the frequency span.

For a newer spectrum analyzer (FSIQ) the number of steps along the frequency axis is for instance 500.

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• This inherently limited frequency resolution need to be considered very carefully when doing measurements.

• For example:

When measuring over a frequency span of 200MHz the 500 frequency points imply that the distance between measurement frequency points is 400kHz.

This can easily cause signals to fall between the measurement points which clearly leads to wrong conclusions.

Great care must therefore be taken to choose the span/RBW correctly.

• Provided that the equipment is operated correctly the use of digital signals provides for other advantages.

Averaging: Digitizing the signal allows us to average over a number of measurements.

Post-analysis: Data may also be transferred to PC for any kind of post-processing.

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Averaging – the video filter

• Averaging is not limited to digital analyzers only, as most analog analyzer include a ”video filter” (Video averaging is another thing (1/n)).

• The video filter is a lowpass filter (band limited video amplifier) that is applied after power detection.

• The video filter smoothes out uncorrelated noise making it easier to detect weak signals.

• The degree of averaging is a function of the ratio between videobandwidth and resolution bandwidth (RBW).

• The optimal video filter bandwidth is normally <1% of the RBW but this may result in unacceptably long sweep times.

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SA limitations – dynamic range

• As the SA operates as a receiver it also displays a limited dynamic range performance.

• Overloading the SA therefore causes distortion inside the analyzer.

• Most prone to this are the mixers in the super-heterodyne chain.

• The input power to the active parts of the SA may be reduced using the internal attenuator.

• For very high input power levels this may not be sufficient .. note that if presented with a sufficiently high input power the input stage of the SA may be destroyed.

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SA limitations – dynamic range - II

• The specific use of input attenuation depends on the specific analyzer.

• In some cases the attenuation is reflected directly on the display.

• For most spectrum analyzers the IF gain is set-up to automatically compensate for changes in the input attenuation.

• As a direct result the signal level remains stable while the noise floor on the other hand is raised with increased attenuation.

The increasecorrespondsto change in input att.

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SA limitations – dynamic range - III

• No matter what approach is used for the input attenuation it affects the dynamic range an hence helps determine the maximum detectable amplitude difference.

• Different definitions exist:

Measurement range (noise floor maximum input power).

Mixer compression (noise floor mixer CP1dB).

Second/Third harmonic (noise floor the input power where the second/third order harmonics are equal to the noise floor) (SFDR).

• A graphical method can be used to determine the optimal input level for each bandwidth setting Optimum Dynamic Range.

• The parameters needed for this may all be obtained from the spectrum analyzer data sheet:

Noise floor at a certain bandwidth (displayed average noise level (DANL)).

Third order intercept point (TOI).

Second order intercept point (SOI).

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SA limitations – dynamic range - IV

• To see how the resulting dynamic range performance of an analyzer may be determined consider the following case:

DANL: -120 dBm/Hz.

TOI: +15 dBm.

SOI: +30 dBm.

Desired Signal Power @ Input

Power level rel. to desired signal

0 dBc

‐20 dBc

‐40 dBc

‐60 dBc

‐80 dBc

0 dBm‐20 dBm

‐40 dBm‐60 dBm

‐80 dBm

• Based on these numbers we need to be able to determine the performance that we can expect from our spectrum analyzer set-up.

• Only when we know the details of the performance can we set-up the measurement to obtain the optimum performance for a specific measurement.

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SA limitations – dynamic range - V

• First step: Add the noise level:

X = DANL, Y = 0 dBc.

If the desired signal is equal to the noise level the difference between noise and desired signal is 0 dBc.

• For a DANL of -120dBm/Hz and a RBW of 10kHz the resulting noise is given as -120dBm/Hz + 40dB = -80dBm/10kHz.




0 dBc

‐20 dBc

‐40 dBc

‐60 dBc

‐80 dBc

0 dBm‐20 dBm

‐40 dBm‐60 dBm

‐80 dBm

100kHz

1kHz

• The noise has a slope of -1:

For each dB increase in the desired signal the difference between the desired signal and the noise floor increases by 1 dB.

• For higher or lower RBW the noise floor moves on the graph.

• Increasing/decreasing the BW by a factor of N raises/lowers the DANL by a factor of 10log(N).

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SA limitations – dynamic range - VI

• The second and third order effects are then added to the graph.

• When the input power equals the TOI, the third order product is “equal” to the fundamental.

• The intersection between the noise curve and the distortion curves denotes the optimum input power for the SA.

• Here noise and SOI set the limit.



0 dBc

‐20 dBc

‐40 dBc

‐60 dBc

‐80 dBc

0 dBm

DR• The slope of the SOI and TOI lines are 1 and 2 respectively:

Second order effects increase by 2dB for each dB increase of the desired signal which gives a net increase 1dB.

For each dB increase in the desired signal the third order intermodulation increases by 3dB net increase of 2dB.

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SA limitations – dynamic range - VII

• For intermodulation measurements with low frequency separation phase noise can become the dominant factor in determining the dynamic range.

• Considering only noise and distortion our graphical model indicates a dynamic range performance of approx. 60dB.

• Here the phase noise places the lower limit by restricting the dynamic range to 50dB.

Desired Signal Power @ Mixer


0 dBc

‐20 dBc

‐40 dBc

‐60 dBc

‐80 dBc

0 dBm‐20 dBm

‐40 dBm‐60 dBm

‐80 dBm

• For instance, consider the case where two tones have a frequency separation of 1kHz and the phase noise level of the analyzer in question, at 1kHZ offset, is -50dBc.

• This means that the dynamic range of the measurement will never be more than

50 dB.

TOITOI

PNPN

Jan Mikkelsen -30-

Measurement uncertainty

• The previous dynamic range graph was calculated based on the fact that the Dynamic Range is limited by noise on one hand, and spurious responses on the other hand.

The upper limit of the Dynamic Range is determined by the input level where the spurious products reach the noise floor.

• However, this will not enable us to measure an externally generated product accurately when the fundamental input power is equal to the optimum input power shown on slide 28.

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Measurement uncertainty - II

• The measurement uncertainty when trying to discern one sinusoid signal from another (at the same frequency) is give as:

where d is the relative difference between the two signals in dB.

• For a maximum uncertainty of 1dB the amplitude difference must be at least 18dB!

• This also influences the dynamic range considerations.

)101log(20 20/ddB ±=Δ

Jan Mikkelsen -32-

Rules of thumb ...

• All active devices produce IMD:

Use attenuators when combining outputs from signal generators.

Another option is to use circulators or hybrids.

• Analyzers are active devices so watch the input levels:

Use the attenuator to suppress high power signals.

• Adjust RBW and VBW to obtain sufficient dynamic range:

Consider your measurement requirements.

Look in data sheets for the analyzer and determine the set-up required for optimum performance (sweep time vs. dynamic range fx.).

• The most important rule of them all ..

Find out what your spectrum analyzer can and cannot do.

Read the bloody manual!!!

Jan Mikkelsen -33-

Power measurements

• The spectrum analyzer is not a true power meter as it measures amplitude voltages.

• The voltages are subsequently converted to dBm assuming a 50Ωreference impedance.

• A power meter measures the dissipated power directly.

• Different methods are used to perform this power measurement:

Thermistors.

Thermocouples.

Square law detection is used in some power meters (although this is not a true power meter).

Jan Mikkelsen -34-

Power meter block diagram

• RF power is converted to DC power and measured in the power meter.

• More accurate than spectrum analyzer (although newer high-end spectrum/signal analyzers have sub-dB accuracy).

• Combine the use of a spectrum analyser with the use of a power meter.

• After combining input signal generators you should “calibrate” the power readings of the generators by measuring the actual power at the input of your DUT.

measuring non-linear amplifiers - aalborg...

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