Diminishing relative jitter in electrooptic sampling of active mm-wave and THz circuits

M. Jamshidifar; P. Haring Bolívar

doi:10.1364/OE.21.004396

1. Introduction

Since the early 80s [1], electrooptic sampling (EOS) emerged as an advanced solution to characterize high frequency structures and devices with an enormous bandwidth. Although electronic measurement systems like microwave network analyzers are the prevalent methods to characterize high frequency components, EOS remains highly attractive given its ultra-wideband device characterization and freely-positionable near field sensing capabilities. The bandwidth of EOS is limited by the sampling laser pulse width and dispersion in the sampling head only, enabling analysis far beyond electrically measurable frequencies. Electrooptic detection of electric fields up to frequencies of several THz has been demonstrated reaching more than 1 THz in near field [2], and more than 100 THz in free space configurations [3]. Such techniques can be combined with photoconductive switches, in order to excite and analyze passive electronic components impulsively. However, this big potential can strongly be degraded for the characterization of active or nonlinear electronic components as in this case impulsive excitation is not applicable. In this case the input signal of a device under test (DUT) is driven by a microwave synthesizer and the bandwidth is severely limited by the relative timing jitter between EO laser sampling and microwave driving unit [4]. Regardless of whether the laser is synchronized to the microwave source or vice versa [5,6], fast timing jitter cannot fully be eliminated given the required finite time constant of the synchronization loop (typically a PLL). Presently, EOS measurements of active or nonlinear mm-wave (sub THz) circuits are restricted to a frequency of 140 GHz only (measurement with lock-in amplifier in [7]). Two approaches have been adapted to date [5,6] which are both fundamentally based on a PLL system. In one alternative [5], microwave generator and laser are configured as master - slave respectively (MM-LS configuration). In this system feedback error signals modify the laser repetition frequency, by adjusting laser cavity length, in order to compensate its deviation from a microwave triggered signal. A finite intermediate frequency IF is chosen, in order to minimize the influence of noise in the measurement. Unfortunately this MM-LS scheme is unable to fully cope with fast-term jitter due to either slow mechanical adjustment of the laser cavity or noise in the feedback error signal which can unlock the PLL. Another approach is to extracting a synchronization signal from laser repetition rate [6,7] and feeding it into the external reference of microwave generator. This laser master – microwave slave (LM-MS) method also faces limitation given to slowness of the PLL synchronization which induces a large time constant while dealing with the ripples and noise in the synchronization signal. Both approaches are incapable to deal with fast timescale jitter within the time constant of the PLL loops, severely limiting the measurement bandwidth. In this paper, we present a new synchronization approach which allows circumventing this problem completely, by conceiving a direct synchronization between laser and mm-wave signals.

2. Experimental setup with new synchronization technique

A simplified schematic diagram of a conventional MM-LS setup is shown in Fig. 1 (a) (see [7] for more details). In such a traditional system a microwave signal generator injects a signal into an ultrafast DUT and the operation of the DUT is analyzed with an EO probe which sampling the electric field on the circuit with femtosecond laser pulses. In this paper we assess the capabilities of such a system by investigating a 65nm CMOS nonlinear transmission line (NLTL) [7] which generates a broad comb of frequencies in the mm-wave and THz ranges. As mentioned earlier, due to imperfection of synchronization, relative time jitter between microwave generator and femtosecond laser pulse, can reduce the measurement bandwidth. In this case, as will be shown later, although the circuit contains frequency components up to a frequency of 300 GHz, the signal is severely influenced by fast timing jitter, which reduces the measured bandwidth to 150 GHz, only. Generally in such a setup a lock-in amplifier is used to amplify the EO signals and reduce the noise in the measurements, but the presence of the jitter in the measured signal leads to IF signals which have a line width broader than the locking measurement time constant, leading to measurement errors [7]. This is particularly problematic, as the most attractive and valuable data at higher harmonics of the NLTL signal deteriorates due to increasing influence of jitter with respect to the harmonic number. To rationalize this effect one can imagine that 1% of jitter in fundamental signal can be magnified to 10% at 10th harmonic. In the analyzed DUT even higher harmonics have to be detected.

Fig. 1 Electrooptic sampling (a) old setup or a conventional MM-LS (LM-Ms) setup with PLL synchronization and microwave source to drive the DUT (b) the LM-LS setup with new synchronization technique, whereby the laser itself generates the microwave signal directly, without a PLL loop.(c) a detailed schematic of the LM-LS setup (b) and the mechanism of generating microwave signal from laser to drive DUT.

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Alternatively, in order to reduce the influence of jitter we introduce a setup with a new synchronization method: The setup is shown in Fig. 1 (b). In contrast to conventional MM-LS or LM-MS systems, the main difference is that the laser is the only source in the setup responsible both for pumping the microwave signal into the DUT and electrooptic probing. This scheme eliminates the use of a microwave synthesizer. In order to excite the circuit, as seen in Fig. 1 (b), a beam of the laser is used to illuminate a fast photodiode, generating an electronic signal with a comb of harmonics of the laser repetition rate (75 MHz). By using a tuned band pass filter at a harmonic of 10 GHz, the microwave excitation signal is selected and amplified to drive the NLTL. The great advantage of this approach is that a slow PLL synchronization loop can fully be eliminated. For frequency selection a rather sharp cavity filter with center frequency of about fc = 10 GHz and quality factor of Q = 200 is used. The filter can select the 134th harmonic of a typical 75 MHz laser repetition rate and rejects the lower and upper harmonics (f_c ± 75 MHz) with approximately 55 dB of attenuation. The spectrum of this signal is shown in Fig. 2. Hence the laser cavity length and consequently laser repetition rate can precisely (1 Hz resolution) be adjusted in the range of 75 to 76 MHz, therefore there is the possibility to utilize an arbitrary tuned filter and adjusting the laser to resonate at a flexibly definable center frequency. The level of this laser generated microwave signal, immediately after filter, is measured at −55 dBm using Tektronix 2755P spectrum analyzer. The signal has been amplified by a LNA and sort of cascaded amplifiers to level of 0 dBm. This signal is delivered into the NLTL after one more amplification stage with 18 dB of gain (see Fig. 1(c)). As this system is self-referencing the circuit excitation path and circuit sampling path to the same laser source, and the temporal paths along both can be chose to be similar or even identical, the influence of jitter can much more effectively be minimized. The only disadvantage is the additional burden of having to modify components when other excitation frequencies have to be used.

Fig. 2 Measured microwave signal generated from femto-second laser pulse in comparison to a signal of Rohde&Schwarz® SMF 100A low phase noise microwave synthesizer. The phase noise of the signals is close to each other.

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Prior to continue with the next stage of the setup and the aim of using an IQ modulator for IF frequency definition, it is necessary to explain shortly the theoretical mechanism of EOS detection in the frequency domain. As shown in Fig. 3, the EO crystal mixes the signal of the DUT, i.e. the NLTL comb of frequencies, with the comb of the laser repetition rate harmonics to down convert to the baseband, where signal detection is performed with the Lock-in amplifier. However, as two combs of harmonics mix together it is relevant to ascertain which frequency combinations are measured at which difference frequency. Notably only carrier frequency combinations which are close to each other are effectively down converted and larger frequency offsets are filtered out with low pass filtering of the balanced detector configuration including photodiodes and amplifiers (see Fig. 1(b)).

Fig. 3 Mechanism of detection and down converting the NLTL (top left) signal by electrooptic sampling in frequency domain. The comb of the NLTL has a spacing of 10 GHz. An IF (50 kHz) is added by an IQ modulator to the carrier frequency. The spacing between adjacent carriers of the laser comb (bottom left) is one laser repetition rate (75 MHz). Only carriers which are close (ω_c from laser and ω_c + IF from the NLTL) to each other are effectively detected at the base band and higher difference frequencies are filtered. The output base band is a replica of NLTL signal at low frequencies (i.e. multiples of the IF).

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For the chosen device and configuration in this setup, since the input microwave signal of the NLTL is generated from a harmonic (134th) of laser repetition rate, EOS detection will mix it with the identical harmonic number (134th) (when IF = 0Hz in Fig. 3) resulting in a complex situation which down converts all NLTL harmonics to DC. As this would prevent a frequency resolved analysis, it is therefore necessary to introduce an intermediate offset (beating IF frequency) between the NLTL input signal (pump) and the laser (probe). In our case, this IF frequency is introduced by using an IQ modulator before the NLTL (see Fig. 1(c)). One should note that using an amplitude modulator (AM), as typically adopted in femtosecond optical setups is prohibitive, given the harmonics generated by AM modulation. The goal is to introduce an IF by shifting the DUT driving frequency by a constant offset with regard to the sampling frequency, while minimizing the influence of sidebands. While this signal is injected into the NLTL, due to nonlinearity, the side bands can generate spurious signals which after EOS detection can be confused with down converted harmonics of the NLTL. Hence, in the following sections we try to study the effect of this sideband in the NLTL signal in order to minimize the artifacts and errors in the measurements. In our case, by careful adjustment of the IQ modulator driving voltages and calibration, a side band reduction to −32 dBc could be achieved, as seen in Fig. 4.

Fig. 4 The output signal of the IQ modulator, before injecting into the NLTL, which is up converted signal (microwave generated by laser) with an IF. The mixing of IQ modulator generates a sideband which also has one IF space from the carrier. The level of this sideband after optimization is reduced to −32dB_c to minimize the artifact while mixing in the NLTL.

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3. Quantitative consideration the effect of side bands on the NLTL signal

As an IF frequency shift can never be perfect, it is relevant to quantify the effect of finite sidebands. In the following section, we evaluate the effects induced by finite sidebands.

The operation of a NLTL can be expressed mathematically as a response function for any arbitrary x input signal with a Maclaurin power series as:

f (x) = \sum_{i = 0}^{\infty} a_{i} x^{i}

Since the NLTL is a voltage controlled phase shifter there is no gain. Therefore an upper bound for the influence of sidebands can be derived under the assumption of a lossless NLTL. Neglecting losses (loss can be considered as a constant in the following calculation), theoretically and from energy conservation theory, the amount of input power delivered to the output is equal but with different distribution over infinite number of harmonics, therefore:

p_{o u t} = p_{i n} \to_{} p_{f (x)} = p_{x}

For a single carrier input:

{\begin{matrix} x = A \cos (ω_{c} t) \\ p_{f (x)} = p_{x} = p_{c} = \frac{1}{2} | A |^{2} \end{matrix}

and for a carrier plus a single sideband (C + SSB) input:

\underset{x}{\underset{︸}{A \cos (ω_{c} t)}} + \underset{Δ x}{\underset{︸}{m \cos [(ω_{m} + ω_{c}) t]}}

while x and Δx are carrier and side band respectively, the input power spectrum is:

p_{x + Δ x} = p_{x} + p_{Δ x} = \frac{1}{2} {| A |}^{2} + \frac{1}{2} | m |^{2}

Provided that modulation index:

‖ \frac{Δ x}{x} ‖ = \frac{m}{A} ≪ 1,

and from Eq. (1) and (4) the NLTL output for C + SSB can be approximated by:

\begin{matrix} f (x + Δ x) = \sum_{i = 0}^{\infty} a_{i} (^{x + Δ x) i} \\ = \sum_{i = 0}^{\infty} a_{i} x^{i} {(1 + \frac{Δ x}{x})}^{i} ≅ \sum_{i = 0}^{\infty} a_{i} x^{i} (1 + i \frac{Δ x}{x}) \\ = \sum_{i = 0}^{\infty} a_{i} x^{i} + \sum_{i = 1}^{\infty} a_{i} . i . Δ x . x^{i - 1} = f (x) + \underset{}{\underset{}{\underset{Δ f (x)}{\underset{︸}{(\sum_{i = 1}^{\infty} a_{i} . i . Δ x . x^{i - 1})}}}} \end{matrix}

It is notable to observe the separation of influences as

f (x)

only reflects the harmonics of the carrier with a regular spectrum at (ω_c, 2ω_c, 3ω_{c, …}), while

Δ f (x)

represents the influence of sidebands. Substituting Eq. (4) in Eq. (6) yields:

Δ f (x) = m \cos [(ω_{m} + ω_{c}) t] \sum_{i = 1}^{\infty} a_{i} . i . {[A \cos (ω_{c} t)]}^{i}

Thus, the spectrum of

Δ f (x)

contains (ω_c ± ω_m, 2ω_c ± ω_m, 3ω_c ± ω_m,…) frequencies, which means that only the first sideband of each carrier (harmonic) needs to be taken into account while the rest can be suppressed.

In terms of the output power spectrum from (6):

p_{f (x + Δ x)} = p_{f (x)} + p_{Δ f (x)}

Since

p_{o u t} = p_{i n} \overset{}{\to} p_{f (x + Δ x)} = p_{x + Δ x} = p_{x} + p_{Δ x}

From Eq. (2), Eq. (3) and Eq. (5) it follows:

p_{Δ f (x)} = p_{Δ x} = \frac{1}{2} | m |^{2}

These results demonstrate that for a small modulation index, the power of the side bands at the output of the NLTL equals to the input side band power and whenever the power of the sidebands is small in comparison to the carrier the effect of sidebands at the NLTL output is negligible.

4. Results

In our experiments with manual optimization (try and error) of the IQ modulator parameters such as IF (I,Q) levels and phase as well as DC offset, a C + SSB signal with RF side band level of $S B L_{d B_{c}} = 20 \log (\frac{m}{A}) = - 32 d B_{c}$ (see Fig. 4), or equally $\frac{m}{A} ≅ 0.025$ is achieved . This SBL fulfills the above mathematical assumption and allows neglecting sideband effects in the NLTL down converted electrooptic signals.

Using LM-LS method, jitter at IF = 10 kHz is measured at ± 3 Hz (drift of 3 × 10⁻⁴) and strongly stabilized down to a few mHz by increasing the IF to 50 kHz (drift on the order of 10⁻⁷). This stability enhancement is a consequence of a reduction of laser phase noise which decreases with increasing offset frequency. In order to emphasize on jitter reduction, comparative results of measurements (only at a slightly different IFs) on a 65 nm CMOS NLTL are shown in Fig. 5. It can be seen that by increasing the harmonic number, the measurement with LM-LS achieves a significant gain and deviates from the measurements with LM-MS due to larger signal to noise ratio. In LM-MS method, the larger jitter at higher harmonic numbers limits the bandwidth of the measurements to the 14th harmonic (140 GHz) and beyond hits the noise floor (see Fig. 5). With LM-LS technique we are able to increase this measurement bandwidth up to 300 GHz (30th harmonic).

Fig. 5 Measured signal of the NLTL output with LM-LS setup and using lock-in amplifier up to 30th harmonic (300 GHz). The injected signal of the NLTL is a microwave signal generated by laser at 10 GHz. Due decreasing jitter, we are able to measure higher harmonics with higher signal to noise ratio. The system sensitivity is restricted by shot noise level which is measured and calculated in [7].

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Having compared with previous synchronization methods, we have also investigated LM-MS configuration in which an external trigger of the microwave generator is obtained from the laser repetition rate by frequency multiplication and division. Using this method the frequency drift at IF = 10 kHz is measured at ± 25 Hz. Theoretically in comparison with ± 3 Hz drift at 10 kHz for LM-LS, S/N ratio decreases by a factor of $- 20 \log (\sqrt{\frac{B W_{L M - M s}}{B W_{L M - L S}}}) = - 20 \log (\sqrt{\frac{25}{3}}) = - 9.2 d B$ and we have measured at −15 dB at 15th harmonic. This effect by enhancing the noise (see Fig. 5) reduces the measurement bandwidth to the 14th harmonic. On the other side jitter in the setup increases proportional to the harmonic number and a drift of 25 Hz at fundamental generates 750Hz drift at 30th harmonic. Since the lock-in measures all harmonics with the same time constant (bandwidth), the higher the harmonics is measured with less the accuracy and we have already shown the setup measurement bandwidth can be decreased to 5th harmonic [7]. It is evident that EOS must be stabilized against jitter while phase noise in the NLTL increases by factor of $20 log (n)$ , (while n is harmonic number), otherwise even a small drift can cause a large error at higher harmonics. Based on these facts we recommend LM-LS setup as a worthwhile alternative for ultrahigh bandwidth electrooptic analysis of active mm-wave and THz circuits due to minimized jitter capability.

5. Conclusion

A Laser Master-Laser Slave configuration was introduced as a new, robust and economic solution to significantly reduce jitter in electrooptic sampling systems. According to comparative experimental results which are performed on a NLTL, It has been proven that the method has significant advantages over previously reported alternative synchronization schemes. Based on the envisaged device under test specifications this method can flexibly be designed and adapted for other EOS applications.

Acknowledgment:

We gratefully appreciate L. Tripodi (Philips Research Eindhoven) and A. Rydberg (Uppsala University) for useful discussions and the provision of the silicon based ultrafast NLTL devices [8]. The work leading to these results was supported with funding by the European Community's Seventh Framework Programme under grant agreement no: FP7-224189, ULTRA project [9].

References and links

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3. C. Kübler, R. Huber, S. Tübel, and A. Leitenstorfer, “Ultrabroadband detecetion of multi-terahertz field transients with GaSe electro-optic sensors: approaching the near infrared,” Appl. Phys. Lett. 85, 3360–3362 (2004).

4. K. S. Giboney, S. T. Allen, M. J. W. Rodwell, and J. E. Bowers, “Picoseconds measurements by free-running electro-optic sampling,” IEEE Photon. Technol. Lett. 6(11), 1353–1355 (1994). [CrossRef]

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9. www.ultra-project.eu

Diminishing relative jitter in electrooptic sampling of active mm-wave and THz circuits

Abstract

1. Introduction

2. Experimental setup with new synchronization technique

3. Quantitative consideration the effect of side bands on the NLTL signal

4. Results

5. Conclusion

Acknowledgment:

References and links

Cited By

Figures (5)

Equations (10)

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