Phase-locked-loop-based delay-line-free picosecond electro-optic sampling system
Gong-Ru Lin and Yung-Cheng ChangCitation: Review of Scientific Instruments 74, 2255 (2003); doi: 10.1063/1.1536256 View online: http://dx.doi.org/10.1063/1.1536256
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Phase-locked-loop-based delay-line-free picosecond electro-optic
sampling system
Gong-Ru Lina)and Yung-Cheng Chang
Institute of Electro-Optical Engineering, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu, Taiwan 300, Republic of China
共Received 7 January 2002; accepted 12 November 2002兲
A delay-line-free, high-speed electro-optic sampling 共EOS兲 system is proposed by employing a delay-time-controlled ultrafast laser diode as the optical probe. Versatile optoelectronic delay-time controllers 共ODTCs兲 based on modified voltage-controlled phase-locked-loop phase-shifting technologies are designed for the laser. The integration of the ODTC circuit and the pulsed laser diode has replaced the traditional optomechanical delay-line module used in the conventional EOS system. This design essentially prevents sampling distortion from misalignment of the probe beam, and overcomes the difficulty in sampling free-running high-speed transients. The maximum tuning range, error, scanning speed, tuning responsivity, and resolution of the ODTC are 3.9共700°兲, ⬍5% deviation, 25–2405 ns/s, 0.557 ps/mV, and⬃1 ps, respectively. Free-running wave forms from the analog, digital, and pulsed microwave signals are sampled and compared with those measured by the commercial apparatus. © 2003 American Institute of Physics.
关DOI: 10.1063/1.1536256兴
I. INTRODUCTION
The high-speed sampling oscilloscope is an extensively used system that enables picosecond resolution for high-speed measurements of repetitive electrical transients. It originates from the development of sampling techniques since the 1950s, however, its use is limited below 10 ps owing to the slow evolution of fast step-recovery diodes. From the beginning of the 1980s, approaches have succes-sively emerged to improve the sampling resolution.1 Joseph-son junction sampling was primarily demonstrated by using a superconducting switch as an electronic sampling gate, which although it has been refined to achieve a temporal resolution of 2 ps, it is still restricted in practical applications due to its requirement of a low-temperature environment. Later, photoconductive sampling 共PCS兲 geometry was dem-onstrated with subpicosecond temporal resolution, microvolt sensitivity, and a larger dynamic range. A photoconductive switch made on semiconducting materials with an ultrashort carrier lifetime is employed as an ultrafast sampling gate in the PCS system. Picosecond optical pulses are then intro-duced to trigger the switch for wave-form sampling. Al-though such a technique exploits jitter-free synchronization in favor of the optical triggering scheme, it still suffers from the limited sampling resolution that is determined by the device geometry and the material parameters of the sampling gate. In addition, the photoconductive gates must be either integrated with the device under test共DUT兲 or fabricated as an external probe tip.2 Electro-optic sampling 共EOS兲 is the latest technique developed, which is unique among the pro-posed sampling systems due to its all-optical configuration. It relies only on electric field coupling between the optical
sampling gate 关i.e., an electro-optic 共EO兲 crystal兴 and the DUT. Hence, it does not remove real charge from the DUT to the sampling gate. The electric field of the DUT results in a change in the birefringence properties of the EO crystal and a rotation of optical polarization. By placing the EO crystal between crossed polarizers, the intensity of the transmitted
共or reflected兲 optical probe beam thus linearly changes as a
function of the electric field strength. With the fast evolution of ultrafast laser technology, an EOS system with sub-picosecond sampling resolution has previously been demonstrated.3
Figure 1 illustrates a typical setup of conventional EOS systems, in which the laser pulse train is divided into pump and probe beams. The pump beam repetitively impulses the DUT, while the probe beam synchronously samples the field-induced birefringence caused by the transient response of the DUT in the EO medium. The pump beam is modulated at a frequency far below the laser repetition rate to facilitate lock-in detection. Alternatively, an electrical pulse generated by an ultrafast optoelectronic switch or a comb generator is used to drive the electrical devices that cannot be optically triggered. The probe beam is passed through an optom-echanic delay line共OMDL兲 to provide a true-time delay with respect to the measured DUT signal.4A variable compensa-tor is added between the crossed polarizers to optically offset the static birefringence of the EO medium for linear opera-tion at 50% transmission. The intensity of the reflected probe beam is measured by a low-speed photodiode to obtain the average response via the integration of pulse trains in the modulating duration. A lock-in amplifier 共LIA兲 is used to measure the amplitude of the modulated intensity, which yields a dc output voltage that is proportional to the ampli-tude of the sampled electrical signal. The LIA facilitates the detection of DUT signals with microvolt sensitivity. The out-a兲Author to whom correspondence should be addressed; electronic mail:
2255
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put signal is either plotted as a function of the delay time or real time displayed on an oscilloscope. This results in an equivalent time representation of the impulse response of the DUT.
Alternatively, unsynchronized sampling based on an in-stantaneous scanning of the relative delay time between the DUT signal and optical probe beam has also been demonstrated.5,6 This is implemented by slightly offsetting their corresponding repetition frequencies, thereby a repeti-tive scanning can be obtained after a number of periods. The schematic diagram of the real-time EOS system is depicted in Fig. 2. The merit is that a ‘‘real-time’’ reconstruction of the high-speed DUT signal can be made on an oscilloscope with a very low sampling rate and frequency bandwidth. Such an offset-frequency sampling technique essentially eliminates the need of the OMDL, which causes the diffi-culty in precise alignment of the optical beam, the measuring
inaccuracy due to misalignment, and the limited scanning speed. However, such a system still suffers from the limita-tion in millivolt sensitivity of oscilloscopes to date.
Subsequently, a delay-time-tunable picosecond Nd:YAG laser has been proposed by employing the phase-shifting technology7to amend the aforementioned problems in a con-ventional EOS system. However, the nonlinear transfer func-tion 共delay time versus tuning voltage兲 of the analog phase shifter used in the laser inevitably leads to a larger sampling distortion during EOS measurement. Therefore, an EOS sys-tem with a better sensitivity by use of lock-in detection, and a linear and quasi-instantaneous scanning measurement with-out the use of the OMDL module is of great interest. Re-cently, a linear phase shifter based on digital phase-locked-loop 共PLL兲 technology has been developed.8 The improvement on the operating bandwidth of the PLL-based phase shifter共hereafter referred as the PLL PS兲 has also been achieved by employing the optoelectronic frequency-downconverting technique.9 By adding a photoconductive switch as the optoelectronic harmonic mixer共OEHM兲 in the PLL, the operating frequency can extend to 20 GHz or higher 共currently limited by the measuring system兲. In this work, we employ the PLL PS as an optoelectronic delay-time controller 共ODTC兲 to replace the OMDL in a conventional EOS system, which eliminates the drawbacks of the OMDL such as low scanning rate and alignment-induced sampling distortion. Versatile configurations of PLL-PS-based ODTC circuits suitable for modifying the EOS system are intro-duced. The performances of the ODTC, including maximum tuning range, linearity, scanning speed, and resolution are determined. By using the different EOS systems proposed in this work, the wave-form sampling of a free-running sinu-soidal microwave signal, a digital signal output from a fre-quency divider 共or prescaler兲, and an electrical pulse gener-ated by the comb generator are demonstrgener-ated.
II. SYSTEM CONFIGURATION A. Design of the PLL PS
The design principle of a PLL PS is based on the modi-fication of a conventional frequency-translated PLL into a frequency-discriminated and phase-tunable delay-locked loop. To achieve frequency discrimination between local clock and free-running DUT signals, several kinds of PLL configurations have been designed for different frequency-tracking schemes, as shown in Fig. 3. For example, two kinds of PLLs for achieving nonoffset frequency synchroni-zation are shown in Figs. 3共a兲 and 3共b兲. In each configura-tion, the frequency of the voltage-controlled oscillator
共VCO兲 is directly frequency synchronized to that of a rf
clock. The drawback of the scheme plotted in Fig. 3共a兲 is the need for high-frequency phase-frequency detectors 共PFDs兲 when operating at high repetition rates. Note that the highest frequency bandwidth of commercially available PFDs is ap-proximately 2.7 GHz. The latter scheme shown in Fig. 3共b兲 is a possible solution that employs the frequency-translation technique by use of frequency dividers. This design essen-tially takes the advantage of recent advances of the
fre-FIG. 1. Block diagram of the conventional synchronous-frequency electro-optic sampling system.
FIG. 2. Block diagram of the real-time nonsynchronous-frequency 共or offset-frequency兲 electro-optic sampling system using a low-frequency-replica technique.
2256 Rev. Sci. Instrum., Vol. 74, No. 4, April 2003 G.-R. Lin and Y.-C. Chang
quency prescalers or dividers 共FDs兲 with a reported band-width of up to 20 GHz. In contrast, Figs. 3共c兲 and 3共d兲 illustrate the block diagrams of mixer-based offset-frequency-discriminated PLLs that are designed for operat-ing at a bandwidth of larger than 20 GHz. In Fig. 3共c兲, two microwave frequency synthesizers are phase locked at an offset-frequency condition. The offset frequency is set by the frequency-divided rf clock, that is, frf⫺ fVCO⫽⌬ f ⫽ frf/N.
For the wave-form sampling of highly repetitive transients, a PLL scheme proposed in Fig. 3共d兲 is more suitable than that in Fig. 3共c兲. The main difference between Figs. 3共c兲 and 3共d兲 is that the latter one benefits from locking of signals with higher repetition frequencies using a low-frequency VCO. This is attributed to both the higher optoelectronic harmonic generation of the fundamental frequency via a gain-switched laser diode 共GSLD兲, and the higher operating bandwidth of the OEHM as compared to the microwave mixer. The pulse train generated from the GSLD consists of a set of super-posed harmonic frequency components, which mixes with the rf clock to generate an intermediate frequency共IF兲 in the OEHM. In addition, to facilitate the capability of high-frequency synchronized operation for the EOS, the latter scheme can further be modified by use of a pair of VCOs to individually drive the DUT and a pulsed laser source for sampling. However, it makes the EOS system complicated, expensive, and bulky.
The basic principle of the PLL PS can be explained by analyzing the phase change of the VCO from the equivalent noise model.9With nodal analysis, we can express the effect of dc reference voltage (VREF) on the phase shift and the
delay time of the output signal from the VCO as
VCO⬇⌽PLL⫺VREF F共s兲K0/s 1⫹KdF共s兲K0/s⬇⌽PLL⫺VREF /Kd ⬅⌽PLL⫺RdVREF ⬅⌽PLL⫹⌬VCO, ⌬t⫽⌬VCO 2 1 frep ⫽ 1 2frep•VREF F共s兲K0/s 1⫹KdF共s兲K0/s ⬵VREF/Kd 2frep ,
wherePLLis the phase noise induced by the PLL, F(s) is the transfer function of the second-order active loop filter
共LF兲 in the PLL, K0 is the VCO gain, Kd is the gain of the PFD, Rd⬇1/Kd 共degree/volt兲 is the phase sensitivity of the PLL PS,VCOis the phase of the VCO, frepis the repetition
frequency of the synchronous signal, and⌬VCOis the phase
shift of the VCO caused by the tuning of VREF. This
ap-proximation sustains only at the PLL passband region due to its relatively large loop gain. It is seen that the phase change of the microwave signals from the PLL-controlled VCO (⌬VCO) is approximately in linear proportion to VREF. The
phase retardation of the microwave signal can, therefore, be linearly and continuously controlled by varying VREFinstead
of using any high-frequency components. In typical PLL sys-tems, it is mandatory to choose a phase detector with a larger phase-gain constant Kd. This, however, will lead to smaller phase sensitivity and a reduced phase-shifting range for our application.
B. PLL-PS-based EOS systems
Early EOS systems sampled the wave form generated from a DUT by simply using two individual microwave/ optical clocks with identical or locked time bases. Today, most of the discrete electronic or microwave/millimeter-wave modules are commonly integrated with individual monolithic frequency sources. This leads to a difficulty in using the conventional frequency-synchronization technique. Owing to such a special requirement, the recently proposed EOS system should also emphasize its design for wave-form sampling of unknown or free-running DUT signals at higher repetition rates. The experimental setup of the proposed delay-line-free EOS system by using ODTC with two offset-frequency PLL PSs, is shown in Fig. 4.10VCO1 and VCO2 with identical frequencies are individually phase locked to the reference clock. VCO1 is used to drive the GSLD for
FIG. 3. Different configurations of electron- or optoelectronic-typed phase-locked loops designed for delay-time control of laser pulses. GSLD: gain-switched laser diode; LF: loop filter; PCS: photoconductive switch; PFD: phase/frequency detector; PS: power splitter; rf PFD: radio-frequency phase/ frequency detector; and VCO: voltage-controlled oscillator.
FIG. 4. Novel delay-line-free equivalent-time electro-optic sampling system using delay-time-controlled laser diode source. PCS: photoconductive switch; GSLD: gain-switched laser diode; VCO: voltage-controlled oscilla-tor; PD: phase detecoscilla-tor; PS: power splitter; and SG: signal generator.
generating the optical pulse train, and VCO2 is used to drive the DUT. The DUT signal is further modulated by an IF synthesizer to facilitate lock-in detection. The phase of the signal output from VCO2 can be linearly and continuously changed with respect to VCO1 via the tuning of the PLL PS controlled by VREF. Since it is also possible to add the
voltage-tuning circuit into the ODTC used with VCO1, the phase of the signal output from VCO1 as well as the delay time of the optical probe pulse can be adjusted alternatively.10,11 The circuit parameters of the ODTC are carefully adjusted to obtain a linear transfer function of the phase shift versus VREF. The effect of the gain of the loop
filter in the PLL on the maximum phase shifting range and linearity is illustrated in Fig. 5. In addition, the phase-tuning gain of the ODTC is set as 100°/V. This corresponds to a delay-time responsivity of 0.557 ns/V. The minimum tuning step that can be monitored by a commercial digital sampling oscilloscope is already smaller than 5 ps共at a voltage tuning step ⬍10 mV兲. Theoretically, the maximum phase shift of the ODTC can be up to 720°, which corresponds to a varia-tion in the delay time of up to 2 periods. The corresponding phase noise spectrum of the GSLD controlled by the ODTC is shown in Fig. 6. In the aforementioned configurations, the use of two frequency-translated PLLs is mandatory since the
frequency synchronization between the electronic/ optoelectronic DUT signal and the optical probe beam must remain. This preserves the high-sensitivity feature of the EOS system that uses the lock-in detection technique.
On the other hand, the aforementioned EOS system can also be simplified to facilitate the characterization of free-running microwave signals from electronic devices or inte-grated circuits 共ICs兲 with internal time bases or oscillators. To meet this demand, two modified ODTCs based on all-electrical frequency-translated PLLs, as shown in Fig. 3共c兲, are employed to control the frequency and delay time of the GSLD source in the EOS system, as shown in Fig. 7. In comparison with the original design, this approach is more compact and easier to be set up since the optoelectronic har-monic mixing module has been replaced by a microwave mixer.
Owing to the recent advances of high-operation-bandwidth FDs, a state-of-the art EOS configuration for real-time measurement without the use of the frequency down-conversion technique can be achieved, as shown in Fig. 8. The dash-line box in Fig. 8 functions as an arbitrary frequency-divided clock. The ODTC-controlled GSLD pulse-train can be frequency locked to the frequency-divided FIG. 5. Phase shift of the PLL PS as well as the delay time of the
ODTC-controlled GSLD pulse train plotted as a function of ODTC-controlled voltage under different gain constants of the filter in the PLL PS.
FIG. 6. Single-sided band phase noise spectra of the VCO in PLL-PS-based ODTC and ODTC-controlled GSLD pulses.
FIG. 7. Schematic diagram or two PLL-based EOS system. GSLD: gain-switched laser diode; LF: loop filter; PCS: photoconductive switch; PFD: phase/frequency detector; PS: power splitter; rf PFD: ratio-frequency phase/ frequency detector; VCO: voltage-controlled oscillator; RFS: reference fre-quency signal; DUT: device-under-test; PBS: polarization beam splitter; PD: photodetector; LIA: lock-in amplifier; SW: electrical switch; and SG: signal generator.
FIG. 8. Schematic diagram of one PLL-PS-based EOS system. GSLD: gain-switched laser diode; LF: loop filter; PCS: photoconductive switch; PFD: phase/frequency detector; FD: frequency divider; PS: power splitter; rf PFD: ratio-frequency phase/frequency detector; VCO: voltage-controlled os-cillator; RFS: reference frequency signal; DUT: device-under-test; PBS: po-larization beam splitter; PD: photodetector; LIA: lock-in amplifier; SW: electrical switch; and SG: signal generator.
2258 Rev. Sci. Instrum., Vol. 74, No. 4, April 2003 G.-R. Lin and Y.-C. Chang
clock of free-running microwave or millimeter-wave signals by use of high-speed FDs. The relative delay time between the microwave and the GSLD pulse-train signals can thus be controlled since there is a linear relationship between the phase of the frequency-divided clock and the microwave sig-nal. Such a design has greatly extended the frequency-discriminating capability of the EOS system with simple cir-cuitry, which is very promising for application in the IC testing industry.
III. SYSTEM PERFORMANCE AND SAMPLING RESULTS
Based on the equivalent-time-sampling theory, the phase change is required to be larger than at least 2for scanning a one-period wave form of a repetitive DUT signal. It is seen from the experimental results that the tuning range of the delay-time-free EOS system can be up to 1.95 periods
共nearly 3.9兲 of the DUT, which is beyond the requirement
of the sampling theory and has already exceeded the records of similar systems.6On the other hand, the tuning resolution of the ODTC is mainly affected by the pulse width of the GSLD, the stability of the phase-tuning circuit, and the tim-ing jitter of the DUT. The GSLD is simultaneously dc biased at the near-threshold condition and driven by an electrical pulse at the desired frequency to generate optical pulses with a full width at half maximum 共FWHM兲 of 15 ps. The short-term stability of the voltage regulator in the ODTC that pro-vides VREFis relevant to the overall timing jitter of the pulse
trains as well as the sampling resolution of the EOS system. To improve the sampling resolution, a smaller optical pulse width via the pulse compression technique, a PLL technique with suppressed timing jitter, and a high-precision voltage regulator with stabilized temperature control, are necessary. As a result, the timing jitter of the ODTC-controlled laser diode is reduced to be 1 ps or less, which also depends on the phase noise performance of the reference source to be fre-quency tracked. The overall performances of the conven-tional and proposed systems are compared in Table I.
The minimum settling time of the ODTC for each step of desired temporal delay of the laser pulse train is 0.1 ms, which is strictly limited by the pull-in and lock-in speed of the PLL-PS-based ODTC. The scanning time for one period of the DUT signal using the ODTC can be expressed as
tp⫽关vtfrept⌬兴⫺1,
where tp is the periodical scanning time of the ODTC,vt is the point-to-point scanning speed, frept is the repetition
fre-quency of the optical pulse train from the GSLD, and ⌬ is the minimum tuning step共i.e., the sampling resolution兲. For example, a periodical scanning time required for the ODTC operated at a repetition frequency of 500 MHz with 1 ps resolution is calculated to be 0.2 s if the scanning speed is 1000 points/s. The scanning speed of the ODTC is relatively comparable with that of the conventional OMDL module. However, the scanning time of the ODTC-based EOS system depends further on the output bandwidth and the integral time of the lock-in amplifier 共which cannot exceed 0.6–1 kHz兲, the executing speed of the controlling program, and the interface between the lock-in amplifier and the computer. This result in an actual tuning speed of 200 points/s or less. Further improvement by use of a high-speed PLL with a shorter pull-in and lock-in time of 1 s or less can be achieved at the possible cost of unexpected phase noise and timing jitter. The minimum tuning step 共i.e., the sampling resolution兲 of the ODTC-based EOS system is about 0.15– 0.2 ps, which is limited by the amplitude noise of the voltage power supply (⌬Vrms⬵0.25 mV兲 for the ODTC circuit. The
temporal resolution of the current apparatus is inversely pro-portional to the repetition rate of the DUT signal. Although the resolution of the ODTC is slightly lower than that of a conventional OMDL-based true-time-delay module (min
⫽2⌬1min/C⬇0.0067 ps with ⌬1min⫽1m兲, such a
resolu-tion under a relatively high sampling rate 共as compared to that of the OMDL兲 is sufficient for most of the picosecond wave-form measurements in the IC testing industry. Thus, the tradeoff between scanning speed and sampling resolution can be made for practical applications.
By using the ODTC-controlled GSLD as the optical source for the EOS system, different kinds of repetitive DUT signals generated from free-running microwave sources and modules such as the frequency synthesizer, frequency pres-caler, and electrical pulse-forming module, are sampled. First, a frequency-synthesized sinusoidal signal at 500 MHz is measured to determine the linearity and sensitivity of the proposed EOS system. The time-resolved wave forms of the DUT signals sampled by a digital sampling oscilloscope
共DSO兲 and the delay-line-free EOS system are shown in Fig.
9 for comparison. The EOS wave form matches perfectly with the DSO wave form except slight deviations caused by the nonlinear response in the delay-time tuning function of the ODTC-controlled GSLD. The wave-form-measurement distortion of the delay-line-free EOS system plotted as a function of delay time is, therefore, compared with the phase-tuning error of the ODTC as a function of tuning volt-TABLE I. Comparisons in performances of ODTC- and OMDL-based EOS systems.
Conventional Ours Tuning range 2
冋
2L c/ 1 frep册
3.9 共theoretically, 4兲 Tuning resolution 6.6 fs ⬃1 ps 共⬍0.2 ps兲 Jitter/phase noise 1.23 ps/⫺115 dBc/Hz at 1 kHz 1.7 ps/⫺105 dBc/Hz at 1 kHz Tuning rate 270–3330 ns/s 25–3405 ns/s Tuning linearity ⬍1% ⬍5%age and is shown in Fig. 10. It is found that the sampling deviation can be controlled within 5% or less, which cor-roborates the phase tuning error of the ODTC共Ref. 9兲 with a maximum value of 8°. This is mainly caused by the finite bandwidth of the PFD, which leads to tuning nonlinearity of the ODTC while operated at the nearly zero-delay region. We have previously mentioned that a further improvement in reducing the sampling deviation relies on the use of an ultra-precise voltage regulator under temperature-controlled con-dition and high-speed PFD with shorter rise/fall time in the ODTC module. In addition, the amplitude fluctuation of the voltage power supply of the ODTC should also be mini-mized since that will cause timing jitter in the ODTC-controlled pulse train. On the other hand, the detection sen-sitivity of the proposed delay-line-free EOS system is about 1 mV/
冑
Hz, which is comparable with that of the conven-tional OMDL-based EOS system.A frequency-prescaled positive-ECL signal共with a divi-sor of 2 or 4兲 driven by the free-running frequency synthe-sizer at 1 GHz was also characterized. Figure 11 presents the nearly identical positive-ECL wave form at 500 MHz mea-sured by either system. It is worth noting that the wave forms measured by the sampling oscilloscope are probably
dis-torted since the ECL signal has to be first offset by using a microwave bias T and then attenuated by at least 10 dB in order to prevent damage of the high-speed sampler in the DSO. Finally, we have also demonstrated the wave-form measurement of a high-speed electrical pulse-train output from a homemade comb generator using a step recovery di-ode共SRD兲. The EOS wave forms of the SRD with a FWHM of 52 ps sampled by EOS and DSO are shown in Fig. 11. It is found that the SRD wave form sampled by the DSO ex-hibits more detailed features, which is mainly attributed to the higher sampling bandwidth of DSO up to 50 GHz
共equivalent to a temporal resolution of about 7–9 ps兲. In
comparison, the EOS wave form of the SRD pulses reveals less featured shapes. This deficiency is more significant as the temporal response of the DUT becomes shorter due to the finite bandwidth of a GSLD-based EOS technique. The tem-poral resolution of the proposed delay-line-free EOS system is similar to the conventional GSLD-based EOS one. In prin-ciple, the time resolution of EOS is decided by statistically independent parameters such as the pulse width of probe beam, the absolute and relative timing jitter of the optical pulse and electrical signal, and the optical/electrical interac-tion times, which can collectively be described as
FIG. 9. Wave form of a microwave signal at frequency of 500 MHz gener-ated from phase-locked VCO2 sampled by using the ODTC-based EOS 共solid line兲 and commercial DSO 共dashed line兲.
FIG. 10. Measured distortion of the modified EOS system and the phase-tuning error of the ODTC plotted as a function of delay time共as well as phase shift兲.
FIG. 11. Wave forms of a digital signal at frequency of 500 MHZ generated from prescaler sampled by using the ODTC-based EOS 共solid line兲 and commercial DSO.
FIG. 12. Wave form of the signal output from a step recovery diode sampled by ODTC-based EOS. Inset plots the same wave form monitored by the DSO.
2260 Rev. Sci. Instrum., Vol. 74, No. 4, April 2003 G.-R. Lin and Y.-C. Chang
total⫽
冑
pw 2 ⫹ j 2⫹ ito 2 ⫹ ite 2 ,where total is the overall response time of the EOS,pw is the FWHM of the optical probe pulse from GSLD,jis the timing jitter from GSLD pulses and DUT signals,itois the
optical interaction time required for the probe beam passing through the EO medium, anditeis the electrical interaction
time of the DUT signal within the spot 共cross section兲 of optical pulses. The optical and electrical interaction times for reflective-type EOS scheme can be expressed as
ito⫽ 2n0H c , ite⫽ W0 c
冑
2 ln 2eff,where c is the speed of light in vacuum, n0 is the refractive
index of the GaAs, H is the substrate thickness, W0 is the
minimum spot size of probe beam, and eff is the effective
dielectric constant of GaAs. In our experiment, the residual timing jitter of about 1.7 ps is mainly contributed by the GSLD pulses since it has been synchronized to the DUT signal. The calculated optical and electrical interaction times were 9.6 ps and 23 fs, respectively. Therefore, the calculated temporal resolution of the current EOS system is approxi-mately 26.8 ps. We conclude that the proposed delay-line-free EOS system would be more practical in noninvasive and
in situ wafer tests than the DSO, however, a less-distorted
determination of the frequency-prescaled wave forms relies on the development of improved ODTC-controlled lasers with ultrashort pulse widths. Nonetheless, the delay-line-free EOS has shown to exhibit superior performances such as a maximum phase shift of up to 700°共corresponding to a delay time of about 3.9 ns and nearly 1.95 periods of a 500 MHz
signal兲, a tuning responsivity of 0.557 ps/mV with sampling error of ⬍5%, and a comparable scanning speed ranging from 25 to 2405 ns/s with highest resolution ⬃1 ps. The compact design of the delay-line-free EOS system without the need of a conventional optomechanical delay line
共OMDL兲 makes this system very promising. Due to the
in-creased requirement of in situ and noninvasive wafer char-acterization, a delay-line-free EOS system without the need of a conventional optomechanical delay line makes it more promising for the very large-scale integrated makes industry. The design and construction of an extremely compact and real-time EOS system using an ODTC-controlled ultrashort pulsed laser diode or fiber laser source has been demon-strated.
ACKNOWLEDGMENTS
This work was supported in part by the National Science Council 共NSC兲 of the Republic of China under Grant Nos. NSC90-2215-E-027-008 and NSC91-2215-E-009-039.
1
J. A. Valdmanis and G. Mourou, IEEE J. Quantum Electron. QE-22, 69
共1986兲.
2R. K. Lai, J.-R. Hwang, J. Nees, T. B. Norris, and J. F. Whitaker, Appl. Phys. Lett. 69, 1843共1996兲.
3A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, Appl. Phys. Lett. 74, 1516共1999兲.
4C.-L. Pan, G.-R. Lin, J.-M. Shieh, C.-W. Tsai, and S.-C. Wang, Int. J. High Speed Electron. Syst. 8, 145共1997兲.
5A. J. Taylor et al., Electron. Lett. 22, 1068共1986兲. 6
J. M. Wiesenfeld et al., Appl. Phys. Lett. 50, 1310共1987兲. 7
C.-K. Johnson and J. Qian, Rev. Sci. Instrum. 61, 1158共1990兲. 8P. V. Brennan, Electron. Lett. 26, 165共1990兲.
9G.-R. Lin, T.-S. Hwang, Y.-H. Chuang, S. C. Wang, and S.-L. Pan, IEEE Trans. Microwave Theory Tech. 46, 1419共1998兲.
10
G.-R. Lin and Y.-C. Chang, Microwave Opt. Technol. Lett. 26, 98共2000兲. 11G.-R. Lin, Opt. Lett. 25, 799共2000兲.
