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Transcript
Pulsed-IV Pulsed-RF Measurements
Using a Large Signal Network Analyzer
Seok Joo Doo*, Patrick Roblin*#, Sunyoung Lee*, Dominique Chaillot*+ and Marc Vanden Bossche+
*The Ohio State University, *+on leave from CEA, +NMDG, # [email protected]
Abstract—A new pulsed-IV pulsed-RF measurement system
using a large signal network analyzer (LSNA) is proposed to
address the problem of desensitization afflicting conventional
pulsed-RF measurement systems. Several extraction methods
using the entire spectrum measured by the system are presented
to extract non-desensitized pulsed-RF S-parameters of a
transistor. The comparison of the calculated S-parameters using
the least-square fitting in time domain with those using only the
fundamental tone reveals the significant increase in dynamic
range achieved by the proposed measurement scheme.
Index Terms—Pulsed measurement, large signal network
analyzer (LSNA), desensitization.
S
I. INTRODUCTION
LOW memory effects are low frequency dispersions
originating from various physical processes in transistors
such as self- heating, parasitic bipolar transistor in FETs, and
traps[1]. It is essential for successful device modeling to
account for these slow memory effects in the acquisition of the
DC and RF device characteristics.
To account for these slow memory effects, pulsed-IV
pulsed-RF measurement techniques have been developed to
reproduce the conditions under which a transistor operates for
large RF signals [2]. Low-frequency memory effects have
indeed a slow time response and the fast pulsed-IV pulsed-RF
measurements maintain a constant temperature, body BJT
voltage or trap state in FETs like when there are excited by
large RF signals. By bypassing slow memory effects, pulsed-IV
pulsed-RF measurements enable us to obtain realistic
isothermal RF characteristics of the FETs.
Most pulsed-RF measurement systems using conventional
network analyzers can only acquire the center tone of the pulse
spectrum and this results in a significant loss of dynamic range
due to the resulting desensitization of 20log(duty_rate).
Typically a 1µs duration pulse with 1% duty rate is used to
avoid low-frequency memory effects [3], and the dynamic
range of the network analyzer for the pulse decreases by 40dB.
The reduction in dynamic range is an important problem which
affects the accuracy of the pulsed measurement data obtained,
especially for low duty rate pulse.
Since the power provided by the center-tone does not reflect
the actual signal RF power applied during the pulse, it is
desirable for more tones in the RF pulse to be included into the
characterization of the DUT. Fortunately, it is possible to get a
large portion of the spectrum of the pulse signal with a large
signal network analyzer (LSNA). Therefore the LSNA can be
expected to improve the dynamic range in the pulsed-IV
pulsed-RF measurement system [4]. The goal of this paper is to
introduce the new pulsed-IV pulsed-RF measurement system
developed using the LSNA, and present the analysis used to
recover the S-parameters from the data measured.
II. PULSED-IV PULSED-RF MEASUREMENT SYSTEM
A. System Realization
In general in pulsed-IV systems both Vgs and Vds pulsed
biases are applied at the gate and the drain of a transistor. In the
experiment reported here, a pulse is only applied at the drain
and a constant DC voltage is used at the gate. It is assumed that
slow memory effects are dominated by self-heating and the
contribution of traps in the gate is neglected. For this entire
study, we have used the Infineon CLY 5 GaAs FET as a DUT.
Fig. 1 shows the pulsed-IV pulsed-RF measurement system
implemented using the LSNA. Port 1 is used for the gate, and
port 2 for the drain. The constant Vgs is applied to the gate using
the LSNA internal bias tee. An external bias tee is used for the
drain. A current sensor consisting of a resistor is used to
measure the drain current with an oscilloscope. A FPGA
digital testbed synchronized to the LSNA [5] was initially used
to synthesize a band-limited pulsed-RF signal using an IQ
modulator. This permitted to address the fact that the
modulation bandwidth of the LSNA is presently limited to 20
MHz. However the 20 MHz bandwidth limitation is not a
major concern for a 0.33µs duration pulse. The final approach
adopted is to use the pulsed RF signal provided by a RF signal
Large Signal Network Analyzer
RF Signal
Generator
PORT1
RF
(RF)
Pulse
Vgs
Power
Supply
Trigger
PORT2
DUT
RF+DC
Bias
Tee
Vds Pulse
Generator
Pulse
Current
Sensor
Fig. 1. Pulsed-IV pulsed-RF measurement system.
Osilloscope
stable. Note that 104 pulses are acquired by the LSNA when
using 95 Hz resolution. Fig. 2 shows a generated RF pulse with
a duty rate of 0.33% and 0.33µs pulse duration.
In addition to generate a RF pulse, the RF signal generator is
also triggering the Vds pulse generator to overlay the RF pulse
upon the drain pulse signal at the proper moment. More details
on the timing for the pulsed-IV pulsed-RF signals are provided
in Fig. 3. The drain pulse has a duty rate of 1% and 1µs
duration which is short enough to achieve the targeted
isothermal condition.
(a) Sinc function in frequency domain (magnitude: white, phase: red).
The main lobe consists of 601 tones with frequency spacing of 9.918KHz.
B. Measurement Bandwidth
To remove the problem of desensitization in conventional
pulsed-RF system, it would be theoretically desirable to use the
entire spectrum of the pulse to obtain higher measurement
accuracy. In practice, however, it is not possible to acquire the
complete spectrum due to the 20MHz IF bandwidth limitation
of the LSNA. Nonetheless by acquiring the spectrum in a wide
enough range we can enhance the measurement accuracy.
According to Parseval’s theorem, the total average power of
the signal x(t ) is the sum of the average power in each
harmonic component:
1
T
T
∫
∞
2
x(t ) dt =
∑C
2
n
∞
∑C
=2
n = −∞
0
2
n
.
(1)
n =0
where C n is Fourier coefficients, and usually has the form of a
(b) RF pulse in time domain (pulse width: 0.33µs, duty rate: 0.33%)
Fig. 2. LSNA pulse measurements at modulation frequency of 9.918KHz and
resolution BW of 95.367Hz. With this setup the LSNA captures 104 pulse
periods for each measurement.
sinc function if x(t ) is a pulse signal. Thus the power included
in the bandwidth range m is
m
power (%) =
∑C
n =1
2
n
∞
∑C
2
n
× 100
(2)
n =1
Fig. 4 shows that the main lobe of a sinc function includes
about 90.3% of the total average power, providing enough
power to essentially suppress the desensitization experienced in
the conventional pulsed-RF system. It is also preferable to
focus only on the main lobe because of the noise floor level of
Fig. 3. Timing for the pulsed-IV pulsed-RF system. Signals (a) and (b)
indicate pulses between the input and output of the current resistor sensor for
the drain (Fig.1), with a pulse width of 1µs and a duty rate of 1%. The RF
signal (c) which is applied to the gate at the measurement time from 0.6µs to
0.93µs, has a 0.33% pulse duty rate.
generator (Anritsu MG3692A) as shown in Fig. 1. The
pulse-modulated signal from this signal generator is very
Fig. 4. As the number of single-sideband (SSB) tones in a sinc function
increases, the included power also goes up. With only main lobe (m=300), it is
possible to obtain the 90.3% of total average power (duty rate: 0.33%,
duration: 0.33µs).
the LSNA. In other words, with resolution bandwidth of
12KHz the noise floor level of the LSNA is typically -70dBm
up to 20GHz when the IF frequency is 10MHz [6], and deep
nulls of the sinc function are usually expected to be below the
noise floor (see Fig.2 (a)).
III. S-PARAMETER ANALYSIS
In this work the system is used to acquire the pulsed-IV
pulsed-RF S-parameters of a RF transistor. For each of the 601
tones ( i ) in the pulsed RF spectrum as shown in Fig. 2 (a), an
S-parameter can be defined as
Fig. 7. Amplitude and phase of S11(ωi) varying tone index. These data are
fitted using the least-square algorithm to recover S11(ω0).
S kl (ωi ) = bk (ωi ) al (ωi ) | (a m≠l = 0) .
(3)
Typical S-parameters resulting for all ω i in the center lobe
are shown (green dots) in Fig. 5.
Fig. 5. Distribution of S-parameters (green dots) for frequencies between
0.97GHz to 1.03GHz for a single pulsed RF measurement at 1 GHz. The blue
‘+’s indicate the S-parameters of the center tone (at 1GHz) in the pulse, while
the red ‘o’s represent the estimated S-parameters recovered by the below leastsquare fitting algorithm in time domain using all tones in the 601 frequency
range specified.
Note that S11 (ω 0 ) and
S 21 (ω 0 ) which are obtained by using only the fundamental
center tone (i=0) will naturally be noisier due to the
desensitization. In Fig. 6, it is shown that the dynamic range of
the center tone decreases by about 50dB.
To estimate the pulse-RF S-parameters based on all the 601
measured tones in the spectrum, three different approaches are
considered.
A. Least-square fit in frequency domain
Because the raw S-parameters S kl (ω i ) are usually noisy, an
estimation of the trend of the S-parameters is needed. It is
reasonable to assume that the S-parameters are basically linear
functions of the frequency within the bandwidth of the main
lobe. Least-square fitting in frequency domain is then used to
find the best fitting straight line. The straight lines fitting the
amplitude and phase of the S-parameter S kl (ω i ) are then used
to predict S kl (ω 0 ) as shown in Fig. 7.
However, as we move away from the center tone in Fig. 7, Sparameters are getting noisier due to the sinc nature of the
spectrum of |a1|. To reduce the impact of the increased noise on
the edge, the least-square algorithm is applied only to a reduced
bandwidth corresponding to 401 tones.
B. Envelope convolution in time domain
Fig. 6. 5-consecutive incident waves for a continuous wave and a pulse signal.
The RF input power is 5dBm. In the case of the pulse signal (duty rate: 0.33%),
the center tone at 600MHz has only -45dBm power, and indicates the 50dB
desensitization.
The signal envelope E[ ] of an arbitrary signal x(t ) can be
recovered from the amplitudes and phases in the spectrum
using
E[ x(t )] = I 2 (t ) + Q 2 (t ) ,
(4)
Fig. 8 shows the recovered envelopes and their convolutions.
The times at which the convolutions E[b1 (t )] * E[a1 (t )] and
E[b2 (t )] * E[a1 (t )] reach their peak gives the group delay
τ S11 = d∠S11 dω i and τ S21 = d∠S 21 dω i of the envelopes of
b1 (t ) and b2 (t ) relative to the envelope of a1 (t ) . In addition
the ratios of E[b1 (t )] * E[a1 (t )] and
E[b2 (t )] * E[a1 (t )]
relative to E[a1 (t )] * E[a1 (t )] give the magnitudes of S11 and
S 21 , respectively.
Fig. 8. The top figure shows the envelope signals E[a1(t)], E[b1(t)] and E[b2(t)]
of the pulsed RF-signals a1(t), b1(t) and b2(t) which are reconstructed from 601
tones spectrum measured. The bottom figure shows the convolution of
E[a1(t)], E[b1(t)] and E[b2(t)] with E[a1(t)].
where I(t) and Q(t) are in-phase/quadrature-phase components
of the signal x(t ) .
After getting the envelopes E[a1 (t )] , E[b1 (t )] and E[b2 (t )] ,
subsequent convolutions between these signals can be used to
extract the device group-delay (τ) and the amplitude of Sparameter using the following equations.
τ S kl = d∠S kl dω i
(5)
S kl (ω 0 ) = E[bk (t )] * E[al (t )] E[al (t )] * E[al (t )]
(6)
50dB
desensitized
signal
Fig. 9. Reconstructed RF signals a1(t), b1(t) and b2(t) for times corresponding
to the center of the pulse. The fundamental tones which are desensitized due to
the pulsing, yield weak signals (dashed lines) with relatively negligible
amplitudes. However the reconstructed signals using all the 601 tones in the
main lobe yields much stronger signals less sensitive to noise.
C. Least-square fit in time domain
The RF signals in time domain can be reconstructed from the
amplitudes and phases of the RF pulse spectrum. Fig. 9 shows
the reconstructed RF signals a1 (t ) , b1 (t ) and b2 (t ) using Eq.
(7). It is obvious that the reconstructed signals (plain line) in the
center of the pulse are much stronger than those of the
desensitized center-tone signal (dashed line). This results from
the fact that the reconstructed signals using 601 tones are
keeping about 90.3% of the original average power. Note that
the decreased dynamic range for a pulse with a duty rate of
0.33% is of about 50dB compared to a CW tone.
A least-square fitting into cosine and sine functions in the
time domain of a1 (t ) , b1 (t ) and b2 (t ) is used to extract the
I and Q components of the signal x(t ) :
x(t ) = I cos(ω 0 t ) − Q sin(ω 0 t )
(7)
This permit us to calculate in turns the amplitude and phase of
S kl (ω 0 ) . As a result of the larger signal amplitude, a reduced
noise is expected in the S-parameters.
In addition to considering the above three analyses,
additional processing steps are required for extracting
S-parameters from LSNA measurements. In distinction to a
conventional network analyzer, the LSNA calibration is not
used for transforming the termination at port 1 and 2 into
perfect match loads. It results that the small reflections from
the coupler and terminations introduce reproducible oscillation
features in the obtained S-parameters if port 1 and 2 are
assumed to be perfectly matched. To remove these unwanted
features one can alternately send an excitation at port 1 and 2.
Obviously these two consecutive measurements must be
performed for the same pulsing conditions. Then solving the
four simultaneous equations obtained from Eq. (8) for both
measurements, gives the error-corrected S-parameters.
⎛ b1, p = S11a1, p + S12 a 2, p ⎞
⎟
⎜
⎜ b2, p = S 21a1, p + S 22 a 2, p ⎟
⎠
⎝
(8)
where a and b are incident / reflected components that are
reconstructed using the least-square fitting in time domain, and
p indicates the primary port (1 or 2) excited .
IV. EXPERIMENTAL RESULTS
A. Pulsed-IV characteristics
Fig. 10 shows the measured pulsed-IV and DC IV
characteristics for the GaAs FET. It is clear that due to
self-heating the DC IV characteristics include the negative
drain conductance at high bias. Typically the FET used has a
maximum thermal resistance ( Rth ) of 35°K/W, and the
observed maximum temperature ( Tdev ) is 93°C for the
gate-source voltage of 0V. But, on the other hand, the
pulsed-IV characteristics bypass low-frequency dispersions as
a result of traps and thermal effects.
Based on the pulsed-IV characteristics, a DC quiescent point
with Vds = 3V and I ds = 350mA is used for S-parameter
measurements.
(a) S11 and S21
Fig. 10. Comparison of pulsed-IV and DC IV characteristics for Vgs from -2V
to 0V in steps of 0.25V. DC IV curves are obtained by a Keithley 4200
semiconductor characterization system, and the developed pulsed-IV system
uses a pulse signal with a duty rate of 1.0%, a duration of 1µs for the drain with
a constant substrate temperature of 25°C. The load-lines for different RF
power levels at 600MHz are also shown.
B. Comparison of S-parameters
Fig. 11 compares the S-parameters obtained using four
different methods:
1) Using only the center tone in the pulses.
2) Using the main lobe in the pulses, and by
- applying a least-square fitting in frequency domain.
- applying a least-square fitting in time domain.
3) Using a continuous wave for a single tone signal.
These data are all averaged over 5 consecutive measurements.
As expected, the S-parameters obtained using center tones
show bigger distortion due to the desensitization. The
S-parameters given by the other methods are smooth functions
of frequency because both for the continuous wave and for the
pulse wave recreated from main spectrum lobe, the
measurements use 100% and 90.3% of the average CW and
peak pulse power, respectively. However, note that the DC IV
(b) S12 and S22
Fig. 11. Comparison of S-parameters for the RF input power of -10dBm in a
frequency range from 600MHz to 2.6GHz with a 10MHz step frequency.
(a) S11 and S21
(b) S12 and S22
Fig. 12. S-parameters with the increased RF input power
characteristics in Fig. 10 are submitted to strong low-frequency
dispersion due to self-heating. To approximately compensate
for this self-heating effect in the continuous wave measurement
of the S-parameters, the gate voltage was arbitrarily adjusted
(by about 0.2 V) to obtain the same DC drain current as in the
pulsed-IV measurement.
Fig. 11 also shows that the
least-square fitting in time domain is better than the fitting in
frequency domain. In addition, note that the small loops
observed in S22 in Fig. 11(b) are reproduced in 5 subsequent
pulsed RF measurements. This reproducible feature indicates
that these loops most likely arise either from the bias-tee
deembedding or a residual calibration error.
To get satisfactory results from center tone extraction, one
may need to increase the output power of the RF signal
generator to compensate for the desensitized power at the risk
of introducing non-linear effects (see self-biasing shift of
load-lines in Fig. 10). Fig. 12 shows the S-parameters for two
different RF input powers. As the RF input power increases, the
S-parameters obtained from the center tone data are notably
stabilized. But even the stabilized S-parameters for the RF
power of 5dBm show more distortion than those extracted by
least-square fitting in time-domain from the main lobe for an
RF power of -10dBm.
It is verified in Fig. 13 that the S-parameters obtained by
least-square fitting in time-domain show good consistency for a
wide range of RF input power. This is largely due to the fact
that the family of tones in the main lobe of the sinc spectrum
provide enough energy to calculate accurate S-parameters. This
measurement benefits also from the fact that the LSNA makes
it possible to measure very small signals with power around
-70dBm.
V. CONCLUSION
(a) S11 and S21
A pulsed-IV pulsed-RF measurement system using an LSNA
is implemented to overcome the problem of desensitization. It
is confirmed that by using a large number of tones in the
spectrum one can reduce the noise compared to using the center
tone only, yielding a more reliable small-signal measurement of
the DUT. This measurement setup could also be easily
modified for the acquisition of pulsed-RF S-parameters for
pulsed-gate voltage to study trap effects in GaN devices.
Finally this LSNA-based pulsed-RF system makes possible the
acquisition of the pulsed-RF harmonic (nω0) response of the
device under various load terminations. In that regard such
non-linear applications would follow in the foot steps of the
work done at IRCOM [7] except that the measurement scheme
used in our approach does not require any modification of the
LSNA hardware.
ACKNOWLEDGMENT
(b) S12 and S22
Fig. 13. S-parameters obtained by least-square fitting in time domain for three
different RF input powers
We would like to thank Jean Pierre Teyssier of IRCOM for
fruitful discussions on pulsed RF measurements. We are
grateful to Dr. Gerald Witt of AFOSR and the State of Ohio for
the support they provided to the development of the
Non-Linear RF Laboratory at OSU.
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