International Audio Laboratories††thanks: The International Audio Laboratories
Erlangen are a joint institution of the University of Erlangen-Nürnberg and
Fraunhofer IIS., Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

# Evaluation of the Speech Resynthesis Capabilities
of the VoicePrivacy Challenge Baseline B1

###### Abstract

Speaker anonymization systems continue to improve their ability to obfuscate
the original speaker characteristics in a speech signal, but often create
processing artifacts and unnatural sounding voices as a tradeoff. Many of
those systems stem from the VoicePrivacy Challenge (VPC) Baseline B1, using a
neural vocoder to synthesize speech from an F0, x-vectors and bottleneck
features-based speech representation. Inspired by this, we investigate the
reproduction capabilities of the aforementioned baseline, to assess how
successful the shared methodology is in synthesizing human-like speech. We use
four objective metrics to measure speech quality, waveform similarity, and F0
similarity. Our findings indicate that both the speech representation and the
vocoder introduces artifacts, causing an unnatural perception. A MUSHRA-like
listening test on 18 subjects corroborate our findings, motivating further
research on the analysis and synthesis components of the VPC Baseline B1.

Index Terms: speaker anonymization, x-vector, bottleneck features, F0, neural
source-filter (NSF), quality evaluation

##  1 Introduction

Numerous developments in the speech signal processing domain have rendered the
collection of speech data as well as its adversarial utilization simpler [1].
As a result, voice privacy is an emerging issue in today's world. Many
technical applications either require by law, or would benefit from, a
preliminary processing to mitigate the risks to user privacy. In this regard,
a VPC has been organized to promote the development of voice anonymization
systems via the introduced baselines, evaluation metrics and attack models,
which are widely adopted by the researchers in the field.

Depending on the downstream task, i.e., the purpose the acquired speech
signals shall serve, the anonymization procedure may be expected to preserve
the prosody and the naturalness. One such use case is a psychiatric support
context where the patients want to stay anonymous [2]. However, the results
from the VPC 2020 and 2022 point out that none of the published systems up to
date can achieve subjective naturalness scores on par with recorded human
speech [3, 4]. Furthermore, our previous work utilizing contrastive systems
revealed that using original x-vectors during synthesis surprisingly yields
worse utility and an increase in the privacy [5]. Therefore, in this work, we
evaluate the speech resynthesis capabilities of the VPC Baseline B1, using
metrics from other domains, to understand if the speech representation and
synthesis block shared across systems of multiple contestants have any
improvement potential.

##  2 Related work

###  2.1 VPC Baseline B1 and its derivatives

The VoicePrivacy Challenge Baseline B1 has been a source of inspiration to
many challenge participants [3, 4]. The system [6], which consists of three
feature extractors, an anonymization block, and a neural vocoder, is depicted
in Figure 1. The feature extractors and their purposes are outlined in the
Table 1.

InputSpeechBNF0anonymizedASRASVOutputSpeechNeural Vocoder(AM-NSF /HiFi GAN
etc.)x-vectorFeatureExtractorsAnonymizeF0 Ext.X-vector poolX-vector

Figure 1: The VPC 2022 Baseline B1.a/b. Table 1: Extracted features per utterance. The quantity in parentheses indicates the resulting tensor shape. N: number of frames of an utterance. W: window size (ms), H: hop size (ms) Feature (purpose) | Extractor | Properties
---|---|---
F0 (Prosody) | YAAPT | (Nx1), W: $35\text{\,}$, H: $10\text{\,}$
BN (Verbal content) | TDNN-F | (Nx256), H: $10\text{\,}$
X-vector (Identity) | TDNN | (1x512)

More than 10 systems are proposed to improve the various aspects of the
baseline over the last three years. Majority of these contributions target the
anonymization block and keep the speech representation or the vocoder intact.
Some however, such as [7], propose alternatives to the bottleneck features.
For the speaker embedding, [8] proposes switching to ECAPA and [9] reports
increased speaker representation capabilities when both ECAPA and x-vectors
are used together.

The NSF, i.e., the neural vocoder, has also received some attention. The 2022
edition of the challenge included two vocoders (NSF-HiFiGAN and HiFiGAN) that
directly predict the waveforms from the speech representation, discarding the
acoustic model (AM) that was present in the 2020 baseline. Works such as [10,
9] use the IMS Toucan toolkit that provides a modular neural vocoder and
utilize local energy in addition to F0 for further prosody control.

###  2.2 Evaluation of voice conversion systems

The voice anonymization problem, especially the way VPC framework treats it,
has some similarities to the voice conversion problem. An overview on voice
conversion mentions intrusive metrics like perceptual evaluation of speech
quality (PESQ) and mel-cepstral distortion (MCD) to evaluate synthesized
speech quality [11]. In our study, the availability of the reference signals
lets us employ such methods. Recently, torchaudio-SQUIM was proposed to
estimate metrics such as PESQ on synthesized speech without needing a
reference [12].

###  2.3 Evaluation of voice anonymization systems

The VPC framework introduced objective and subjective metrics to evaluate
different aspects of the anonymized speech signals [13]. The word error rate
(WER), whose lower values indicate a better utility, is measured by an
automated speech recognition (ASR) system. An automated speaker verification
(ASV) system is used to measure the anonymization success, where higher equal
error rate (EER) values indicate better anonymization. Prosody retention to a
certain extent is ensured by a lower bound on F0 correlation and finally, a
gain of voice distinctiveness measures whether the speaker diversity of the
input speech datasets are preserved by the anonymization process. However,
none of the introduced objective metrics can successfully measure the
perceived naturalness thus the challenge organizers have resorted to a
subjective evaluation of the utterances [13].

The VPC community uses contrastive systems [14, 7, 5], an idea similar to the
ablation studies performed by the machine learning community. A contrastive
system is a marginally different configuration of the anonymization system
that provides further insights into how different modules thereof contribute
to the performance. The cited studies use VPC metrics to assess the privacy
versus utility (ASR scenario) tradeoff and also reported that synthesis with
original set of features cause an increase to EER as well as to WER, hinting
that some artifacts are introduced by the analysis-synthesis pipeline.

To conclude, the existing objective metrics of the VPC do not account for
naturalness. The alternative, subjective listening tests, are non-ideal
because they are time-consuming and costly. Furthermore, the evaluation
methods in the VoicePrivacy literature are not capable of detecting abnormal
behaviors in time, which in our opinion is necessary to find what causes
unnatural outputs. To go beyond the contrastive system studies with EER and
WER, we decided to investigate whether intrusive metrics and their non-
intrusive estimates could be exploited.

##  3 Methodology

###  3.1 Dataset

Table 2: VPC data subsets [13] utilized in this work. #F, #M: number of unique female/male speakers Subset Name |  #F |  #M |  #Utterances
---|---|---|---
libri-test-{enrolls,trials} | 15 | 15 | 1934
vctk-test-{enrolls,trials} | 15 | 15 | 12048

We use the VPC datasets libri-* and vctk-* for our evaluations. A summary of
their content is provided in Tab. 2. These datasets are resynthesized using
the systems in Table 3. The system B1b-spk is the same as the 2022 baseline,
except it uses the original speaker-level x-vectors for synthesis. The system
B1b-utt, using the utterance-level x-vectors for synthesis, imitates the
training conditions of the neural vocoders. Both systems were trained using
HiFiGAN discriminators. The system joint-hifigan-spk denotes the alternative
vocoder (HiFiGAN [15]) provided by the VPC organizers. The system am-nsf-spk
is the baseline used in 2020, that features an additional autoregressive AM
that converts the speech representation into mel-spectrograms. The system mel-
nsf-spk bypasses the AM and performs synthesis using the mel-spectrograms
computed from original utterances, also referred to as copy-synthesis [16]. We
feature both the PyTorch variant (denoted with a suffix -pt) and the C-based
implementation utilized in VPC 2020\. We also included an anchor equivalent
mel-nsf-spk-4k that sets the mel-spectogram values for frequency bands with
$f_{c}>$ $\mathrm{4}$kHz to zero.

A number of pre-processing steps are performed before the evaluation. Systems
we evaluate introduce different amounts of delay, so we align the outputs with
the references using cross-correlation. Many of the utterances contain
silence, as well as some pauses, hence we ran Silero voice activity detection
[17] on the references and computed the metrics on the segments with voice.
Also, a number of utterances were visually inspected to ensure that the
synthesis procedure preserves the loudness, which could bias the evaluation
scores [18].

Table 3: Systems evaluated in this paper. The x-vectors are not anonymized to assess the resynthesis capability. Vocoders are VPC PyTorch implementations, unless noted in the table. ID | X-vector | Vocoder
---|---|---
mel-nsf-pt-spk | speaker-level | NSF
mel-nsf-spk | speaker-level | (C-based) NSF
mel-nsf-spk-4k | speaker-level | (C-based) NSF
am-nsf-spk | speaker-level | (C-based) AM \+ NSF
B1b-utt | utterance-level | joint NSF (+HiFiGAN-D)
B1b-spk | speaker-level | joint NSF (+HiFiGAN-D)
joint-hifigan-spk | speaker-level | joint HiFiGAN

###  3.2 Objective evaluation metrics

We adopt four different objective metrics to evaluate the resynthesis
capabilities. These metrics are all intrusive, meaning that their computation
requires access to a reference signal.

####  3.2.1 MCD

MCD is used to measure the signal similarity in a perceptual sense. The
implementation we use is provided by [19].

####  3.2.2 SI-SNR

scale-invariant signal-to-noise ratio (SI-SNR) is used to measure the signal
similarity [20]. The reference signal is first projected on the estimated
signal, to obtain a scaling coefficient. Then the signal-to-noise ratio is
computed. The implementation we use is a NumPy port of [21].

####  3.2.3 PESQ

PESQ is an intrusive measure introduced by ITU to predict the subjective
speech quality evaluations. We use the implementation in python-pesq [22].

####  3.2.4 GPE

Gross pitch error (GPE) is a metric for F0 extractor evaluation. In our work,
we use it to compare the synthesized F0 to the original. We adopt the
definition in (1), also used in a previous work of us [5].

$\text{GPE: }\frac{\text{num. of frames whose error}>20\%}{\text{num. of
correctly identified voiced frames}}$ (1)

MCD, SI-SNR and GPE have the advantage that they could be computed on smaller
segments.

###  3.3 torchaudio-SQUIM

In addition to the intrusive metrics, we also tested the torchaudio-SQUIM
[12], which provides non-intrusive estimates of the intrusive metrics. We use
their PESQ prediction and report numbers for all the classes as well as for
the reference signals. If these estimates correlate well with their intrusive
complements or with user preferences, SQUIM could be also tested for
evaluating anonymized speech.

###  3.4 Subjective listening test

We conducted a MUSHRA-like listening test on 18 subjects of varying listening
test experiences, using webMUSHRA software [23]. We randomly picked eight
utterances from libri-test and six from vctk-test, (7 male and 7 female
speakers, utterance lengths between $[5.5,8]$ seconds), which are available at
111https://audiolabs-erlangen.de/resources/2023-VPC-resynth-eval. The users
are presented each synthesis output and asked to rate the naturalness using
the following prompt, inspired by the VPC subjective test [13].

You will listen to a series of audio samples, comprising of both original
recordings (referred to as reference) and versions that have been
resynthesized using different neural vocoders, resulting in varying degrees of
artifacts. Your task is to rate the naturalness of each recording.

Naturalness: Please judge how much audio degradation you can hear in each
file. You need to select a score in the interval $[0,100]$, where higher
numbers correspond to a more natural sounding audio, a $0$ corresponding to
'severely degraded' and a $100$ to 'no degradation at all'. For this score
please only consider the sound characteristics and not the content. Also note
that the reference contains some background noise. Finally, the deviations
from original speaker's voice also count as degradations.

##  4 Results and Discussion

###  4.1 Objective evaluation

05101520MCD ($\downarrow$)mel-nsf-pt-spkmel-nsf-spkmel-nsf-spk-4kam-nsf-
spkB1b-uttB1b-spkjoint-hifigan-spk$-$30$-$25$-$20$-$15$-$10$-$50SI-SNR [dB]
($\uparrow$) Figure 2: Evaluation results for signal similarity metrics.

####  4.1.1 Signal similarity metrics

Figure 2 depicts the SI-SNR and MCD results. We saw no significant differences
during visual inspection of the "per-dataset" and "per-gender" distributions.
Therefore we display averages over datasets and gender instead.

Copy synthesis, e.g., mel-nsf-spk, outperformed the others, but mel-nsf-pt-spk
and mel-nsf-spk, two implementations of the same system, behaved differently.
PyTorch copy-synthesis achieved better SI-SNR and MCD. The anchor, i.e., mel-
nsf-spk-4k, attained comparable SI-SNR but the worst MCD. Other vocoders
attained a similar MCD, standing between the copy synthesis and the anchor. We
interpret the discrepancy between mel-nsf and synthesis from the
representation as a sign of inadequacies of the utilized speech
representation, resulting in some further information loss on top of the
artifacts due to NSF. am-nsf-spk performed slightly better than other
vocoders, indicating the AM contributed to the resynthesis performance.

####  4.1.2 F0 similarity

In a similar manner, Figure 3 depicts the GPE results. Behavior across female
and male recordings are shown this time.

mel-nsf-pt-spkmel-nsf-spkmel-nsf-spk-4kam-nsf-spkB1b-uttB1b-spkjoint-hifigan-
spk010203040GPE [%] ($\downarrow$)femalemale Figure 3: F0 similarity
evaluation.

NSF-based systems maintained a certain standard in terms of F0 preservation,
due to the source-filter model. HiFiGAN takes some extra liberty whilst
synthesizing the signals, thus attained significantly higher GPE and this
probably explains why it attained the worst SI-SNR too. An interesting outcome
is that female speech has slightly higher GPE for NSF, but HiFiGAN corrupts
pitch significantly more for male speakers.

####  4.1.3 PESQ and torchaudio-SQUIM

Finally, we compare the PESQ computations as well as PESQ estimates by
torchaudio-SQUIM in Figure 4.

mel-nsf-pt-spkmel-nsf-spkmel-nsf-spk-4kam-nsf-spkB1b-uttB1b-spkjoint-hifigan-
spk1234PESQ ($\uparrow$)mel-nsf-pt-spkmel-nsf-spkmel-nsf-spk-4kam-nsf-
spkB1b-uttB1b-spkjoint-hifigan-spkreferencePESQ-SQUIM ($\uparrow$) Figure 4:
Evaluation results for PESQ and torchaudio-SQUIM estimate of PESQ.

PESQ with respect to the reference (left) shows a similar, but a more
pronounced version of the trend in the SI-SNR plots. PyTorch copy-synthesis,
i.e., mel-nsf-pt-spk, attained the best PESQ scores. The anchor performed
better than the variants that synthesize from the speech representation (e.g.,
B1b). am-nsf-spk performed slightly better than other vocoders, again hinting
the joint AM-NSF approach introduced in 2022 causing minor degradation. joint-
hifigan-spk performed the worst. On metrics that take the perceptual aspects
into account, such as MCD and PESQ, B1b-spk performed better than B1b-utt,
which imitates the vocoder training scenario. This may indicate an underfit. A
number of factors could have caused this, such as an insufficient
representation complexity, lack of augmentation (augmenting x-vectors might
help the vocoder to better learn the neighboring relations of the x-vectors)
or may simply indicate that the training procedure has been cut off too early.
The NSF was trained using L1 loss [6] on the magnitude spectrogram, which
could be substituted with a perceptual loss to improve the performance.

Interestingly, the PESQ scores exhibit a greater inter-utterance variance for
mel-nsf-spk variants. Additional investigations are required to understand
this phenomenon. In particular it is crucial to understand if a confounding
variable affects the scores, as previously shown by [18] with PESQ for factors
such as loudness and alignment.

Torchaudio-SQUIM estimates of PESQ showed a different behavior. Systems joint-
hifigan-spk, B1b-utt and B1b-spk achieved better performance with torchaudio-
SQUIM evaluation. The systems have the HiFiGAN discriminators in common, which
possibly explains the outcome. Some systems, e.g., am-nsf-spk, showed an
unexpected bimodal distribution that is not explained by the gender or the
dataset, which needs further investigations. The SQUIM estimates for the
reference signals, depicted by the right-most violin plot in the Figure 4,
again show a bimodal behavior.

###  4.2 Subjective listening test

The listening test responses are filtered such that the answers for an
utterance, whose reference was rated with less than $90$ points, are removed.
This results in at least $14$ subjects rating each utterance. The ratings are
presented in Figure 5.

mel-nsf-pt-spkmel-nsf-spkmel-nsf-spk-4kam-nsf-spkB1b-uttB1b-spkjoint-hifigan-
spkreference020406080100Score ($\uparrow$)
Figure 5: The subjective evaluation results.

Subjects reported that some mel-nsf-spk utterances had a severe muffling
effect, often at their beginnings, rendering the part of the utterance
completely unintelligible. In contrast, the mel-nsf-pt-spk was reported to
suffer from random impulsive artifacts, somewhat like a "sizzling frying pan
constantly accompanying the recordings". joint-hifigan-nsf was reported to
change the accents, "Americanizing" the voices, and the identity perception
was different to what reference or other systems evoked. Otherwise the speech
was reported to sound most human-like.

Now turning to the analysis of the gathered scores, most subjects were able to
identify the reference stimuli and grade accordingly. Removed answers
constitute less than 10% of the acquired data. The anchor mel-nsf-spk-4k was
rated the lowest whereas joint-hifigan-spk was rated the best, except it
compromises on the speaker identity. Systems other than joint-hifigan-spk
exhibited a higher inter-utterance variance. Notwithstanding the few
utterances with unintelligible segments causing a second modality at the
bottom, the copy-synthesis, mel-nsf-spk was rated the second best, followed by
B1b variants. mel-nsf-pt-spk and am-nsf-spk were rated only slightly better
than the anchor.

####  4.2.1 Predictability of the subjective test scores

Intrusive metrics could not predict the outcome that joint-hifigan-nsf would
be perceived the most natural, B1b performing better than am-nsf-spk and mel-
nsf-spk outperforming mel-nsf-pt-spk. Only evaluation we ran that anticipated
this outcome was torchaudio-SQUIM. We conclude that, the reference being
available causes the intrusive evaluation to focus on the differences in
signals that our subjects did not consider. Among the objective metrics, MCD
was relatively successful.

Comparison of the PyTorch-based mel-nsf-pt-spk and C-based mel-nsf-spk, our
subjects rated the latter better. The subjects penalized non-stationary
artifacts less. To conclude, even though the objective metrics we utilize in
this paper contribute to understanding how the blocks interact, these are not
sufficient to explain the subject preferences completely.

###  4.3 Future work

We think it would be worthwhile to study the effects of using additional
speaker embeddings such as ECAPA [24], as multiple systems in the literature
utilized it and performed well in the VPC 2022\. Part of ECAPA's success comes
from a better temporal pooling strategy using attention. However, VPC simply
uses temporal averaging to obtain the utterance-level x-vectors, and mere
utterance averages to obtain speaker-level x-vectors, so modifications to
these aspects are worth investigating.

Some of the metrics we used, e.g., MCD, GPE and SI-SNR allow computation on
very small segments, unlike PESQ. The time segments with the reported muffling
effect could be automatically located with these and further analysis could be
conducted. Also for these metrics, different temporal pooling strategies could
be experimented with.

##  5 Conclusion

In this paper, we have investigated the reproduction capabilities of the
VoicePrivacy Challenge Baseline B1 by utilizing a diverse set of objective
evaluation metrics. Our subjective and objective evaluation results indicate
that the copy synthesis scores better than the synthesis from representations,
likely indicating the speech representation is causing additional information
loss and yielding unnatural sounding output. Previous studies found that a
more recent speaker embedding could help improve the anonymization
performance, and our results hint that it could also improve the synthesized
speech quality. In addition, the vocoder training scheme may benefit from a
number of changes to bolster its understanding of the speaker embedding space.

The objective metrics we utilize in this work show limited effectiveness in
evaluating the system behavior for anonymization, primarily because they are
intrusive and no references are available for anonymization, and metrics we
evaluated partially align with the listening test subject preferences.
Torchaudio-SQUIM's PESQ implementation performed relatively well, and it does
not require a reference, so the voice anonymization evaluations may benefit
from it.

## References

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  *[VPC]: VoicePrivacy Challenge
  *[NSF]: neural source-filter
  *[F0]: fundamental frequency
  *[BN]: bottleneck feature
  *[AM]: acoustic model
  *[PESQ]: perceptual evaluation of speech quality
  *[MCD]: mel-cepstral distortion
  *[WER]: word error rate
  *[ASR]: automated speech recognition
  *[ASV]: automated speaker verification
  *[EER]: equal error rate
  *[SI-SNR]: scale-invariant signal-to-noise ratio
  *[GPE]: Gross pitch error


††thanks: Tel: +82-10-7517-2711

# A fabrication of low power distribution system for muon $g-2$/EDM experiment
at J-PARC

E. WON  WOODO LEE<EMAIL_ADDRESS>Department of Physics, Korea
University, Seoul 06130, Korea

###### Abstract

The J-PARC muon $g-2$/EDM experiment aims to measure the muon magnetic moment
anomaly $a_{\mu}=(g-2)/2~{}$ and the muon electric dipole moment (EDM)
$d_{\mu}$. The target sensitivity for $a_{\mu}$ is a statistical uncertainty
of $450\times 10^{-9}$, and for $d_{\mu}$ it is $1.5\times 10^{-21}$
$e\cdot\rm{cm}$. The readout electronics require a DC to DC converter to
provide 1.5 V and 3.3 V electric voltage within a specific environment. To
capture the positron decay from the muon, the detector components are placed
in the muon storage area where 3 T magnetic field is applied in a vacuum. The
extra magnetic field from the converter should be less than 30 $\mu$T to reach
the aforementioned sensitivity on $a_{\mu}$. In addition, the electric field
produced by the converter has to be as small as 1 V/m to also reach the target
sensitivity on $d_{\mu}$. For this purpose, we develop a step-down converter.
We discuss the development process and the performance of our DC to DC
converter for the J-PARC muon $g-2$/EDM experiment.

DC to DC converter, Buck converter, Power electronics, Muon, Magnetic moment

##  I INTRODUCTION

The J-PARC muon $g-2$/EDM experiment 10.1093/ptep/ptz030  aims to measure the
muon magnetic moment anomaly $a_{\mu}=(g-2)/2~{}$ and the muon electric dipole
moment (EDM) $d_{\mu}$, which requires a specific low direct current (DC)
power distribution system with a minimum stray field generation of as low as
30 $\mu$T and 1 V/m in the muon orbit system. It also has to provide
appropriate electric powers to the readout system under a strong 3 T magnetic
field. Here we develop a DC to DC converter that meets all the requirements
from the experiment. The muon $g-2$/EDM experiment detects positrons with
silicon detectors, and the electric readout system requires DC power
distribution for its operation. The DC to DC converter is designed to generate
various DC outputs under a strong static magnetic field. Our design of the DC
to DC converter utilizes buck converter DCDC  as well, which is commonly used
in high energy physics CMSDCDC ; JPARCDCDC . However, our design is carefully
optimized to mitigate the stray magnetic field for the experiment, and we
discuss the design details in the following sections.

##  II Requirements and design

There are several requirements in the design of the DC to DC converter for the
J-PARC muon $g-2$/EDM experiment. First, appropriate electric power must be
delivered to the readout electronics. Second, in the design of the converter,
the space limitation due to the geometry of the detector system, including the
readout electronics, must be carefully considered. These requirements allow us
to use only limited board geometry and electric components. They will be
discussed in the following sections.

###  II.1 Electric power requirements

The DC to DC converter has to provide electric powers to four Application
Specific Integrated Circuit chips (ASICs), one Field-Programmable Gate Array
(FPGA), and one optical transceiver for the operation of the readout electrics
system of the experiment. Each receives different voltages and current values
for the operation, and they are summarized in Table 1. Both an optical
transceiver and a FPGA receive 1.0 A and 3.3 V. However, for ASICs, they
receive 0.9 A and 1.5 V. The DC to DC converter is designed to provide stable
electric power of $8$ W in total, to the readout system.

Electric power consumption list
---
Component | Current (A) | Voltage (V)
Optical transceiver | 1.0 | 3.3
ASICs | 0.9 | 1.5
FPGA | 1.0 | 3.3
Table 1:  List of electric components in the readout system that receives
electric powers from the DC to DC converter. Both an optical transceiver and
an FPGA receive 1.0 A and 3.3 V. However, ASICs receive 0.9 A and 1.5 V.

###  II.2 Space requirements

The positron detector modules in the $g-2$/EDM experiment are placed in the
cylindrical storage under a uniform magnetic field. In total, 40 detector
modules will be mounted in radial direction like vanes, as shown in Fig. 1.
Each vane has the following structure. The central part consists of the strip
silicon sensor, and two readout systems are placed at the top and bottom
position of silicon strip sensor arrays. The DC to DC converter will be
mounted at the top and bottom of the readout system. Due to this geometrical
configuration, the height of the DC to DC converter should be smaller than the
gap between each vane. Along with this constraint, the size of the converter
should be as small as 37 $\times$ 180 $\times$ 150 $\rm{mm^{3}}$ for the
height, the width, and the length, respectively.

Figure 1:  The positron detector consists of in total 40 modules. One module
contains four arrays of silicon strip sensors. The distance from the center of
the DC to DC converter to the vane center is $435$ mm.

###  II.3 The board design

Our board has two main stages according to its electric functionality and are
shown in Fig. 2. The $V_{in}$ is defined as the input voltage for the DC to DC
converter at the first stage in this figure. The first stage is composed of a
switching type DC to DC converter. Due to the fact that high current is
applied to the first stage, we choose this switching type of DC to DC
converter to minimize the electric power loss. We choose to use a product from
Texas Instrument of the model TPS53318 TPS53319  in order to achieve high
efficiency in a high current environment. The TPS53318 chip drops down
$V_{in}$ to $V_{tps}$, and $V_{tps}$ is defined as the output voltage of the
TPS53318. Note that switching type converters require an associated inductor,
and this forces us to design an inductor carefully. We discuss it in the next
section. The value of $V_{tps}$ is set to 4.88 V, which is the minimum voltage
that the linear regulators can receive at the second stage. At the second
stage, the current is divided into three different channels, and the output of
each channel is directly connected to the electric devices in the readout
electronics. We choose three different linear type regulators for suppressing
electric noise. The outputs of the regulators are 1.5 V, 3.3 V, and variable
DC voltage, which are referred to as $V_{1}$, $V_{2}$, and $V_{3}$. The
specifications of the TPS53318 chip and three linear regulators are summarized
in Table 2.

The size of Printed Circuit Board (PCB) and its number of layers for the DC to
DC converter are designed to satisfy the space and electric requirements as
discussed above. Figure 3 shows the fabricated PCB. The area of the board is
determined to be 180 $\times$ 150 $\rm{mm^{2}}$, and the board has four layers
for routing signals and grounds to all the components.

Figure 2:  The design diagram for the low power distribution is shown. We
design the low-power distribution system with two distinct stages. The
TPS53318 is for the first stage and three different linear regulators are for
the second stage, and outputs are to be delivered to the readout electronics.
Figure 3:  The PCB for the DC to DC converter is shown. The board consists of
4 layers, the thickness of the board is $1.5~{}\mathrm{mm}$. There are two
middle layers between the top and bottom layers. The middle layers are for
input, output power, and ground.  Main IC chips for DC to DC converter
---
IC |  $V_{in}$ (V) |  $V_{out}$ (V)
TPS53318 | 6.50 $\sim$ 22.00 | 0.6 $\sim$ 5.5
LMS1587-3.3 | 4.75 $\sim$ 7.00 | 3.3
LMS1587-1.5 | 3.00 $\sim$ 7.00 | 1.5
LMS1587-Adj | 2.75 $\sim$ 7.00 | 1.5 $\sim$ 5.8
Table 2:  The specifications of main Integrated Circuit (IC) chips for DC to
DC converter are shown. The TPS53318 is for the first stage, and three
different linear regulators (LMS1587 series LMS1585 ) are for the second
stage, and outputs are to be delivered to the readout electronics.

###  II.4 The inductor design

Our DC to DC converter is required not to introduce the magnitude of the stray
magnetic field of more than 1 parts per million (ppm) 10.1093/ptep/ptz030  of
the 3 T static magnetic field. Because of this, the commonly used ferrite core
inductor cannot be used since the ferrite core itself is magnetized, resulting
in the production of the stray magnetic field. The second problem is that its
inductance is changed by the external magnetic field. This may results in the
faulty operation of the DC to DC converter. An air-toroidal inductor (ATI)
with a copper coil is fabricated instead of the ferrite core to avoid these
problems. The suitable physical size of ATI, which is limited by the gap
between two adjacent vanes, is discussed in this section. The required
inductance ($L$) of ATI for given maximum output current ($I^{MAX}_{out}$),
switching frequency ($f_{sw}$) of the converter, maximum input voltage
($V_{in}^{MAX}$) from our DC to DC voltage is provided by the company TPS53319
following formula

$L=\frac{3}{I^{MAX}_{out}\cdot f_{sw}}\cdot\frac{(V_{in}^{MAX}-V_{tps})\cdot
V_{tps}}{V_{in}^{MAX}}.$ (1)

Figure 4 shows the relationship between $L$ and $f_{sw}$ when we assume other
values to be for $V_{tps}$ = 4.88 V, $V_{in}^{MAX}=22~{}\mathrm{V}$, and
$I^{MAX}_{out}=8~{}\mathrm{A}$ (they are allowed maximum values of given
chip). Since the minimum $f_{sw}$ of our chip is 250 kHz, and the power loss
from the switching is minimized with the lowest $f_{sw}$, our target $f_{sw}$
is set to 250 kHz and this results in our target value of $L$ as
$5.70~{}\mu\rm{H}$ according to Fig. 4.

Figure 4:  The expected inductance $L$ as a function of $f_{sw}$ is shown.
Note that the recommended range of $f_{sw}$ according to the company is from
250 to 970 kHz.

There are three parameters that determine the inductance value of the ATI
($L_{ATI}$). They include the outer radius ($R$) from the center of the coil
to the center of the cross-section and the radius of the cross-section ($r$)
itself. The third parameter is the number of turns ($N$) of the coil.
Considering the height limitation between the DC to DC converter to the next
vane, we choose $r$ to be 7 mm. Considering the area of the converter, we
choose $R$ to be 8.6 mm. This gives us $L_{ATI}=5.70~{}\mu\rm{H}$ with $N$ =
40. Figure 5 shows the relationship among $r$, $R$, and $L$ when $N$ = 40.
There may be other sets of solutions for the target inductance, but it is not
important for similar values of $r$ and $R$, so our default values for
$L_{ATI}$ are set to be these values.

Figure 5:  A relationship among $r$, $R$, and $L$ with $N$ = 40 is shown. The
target point with $L$ = 5.70 $\mu\mathrm{H}$ is shown as a circle.

##  III Simulation

###  III.1 Electric circuit simulation

The electric characteristic of the DC to DC converter is studied by the PSPICE
simulation allegro . Our simulation estimates the time structure at a
transient-state and the voltage fluctuation. This simulation also aims at
studying the stability of $V_{tps}$, $V_{1}$, $V_{2}$, and $V_{3}$ when
$L_{ATI}=5.70~{}\mu\mathrm{H}$ and at a steady-state. The DC to DC converter
enters to transient-state at $0.42~{}\rm{ms}$ from the power turns on, and
after that, the DC to DC converter becomes a steady-state from
$0.82~{}\rm{ms}$ as shown in Fig. 6. The three outputs from linear regulators,
$V_{1}$, $V_{2}$, and $V_{3}$ become a steady-state after $V_{tps}$ becomes
stable. The $V_{1}$ goes into a steady-state first because it requires the
minimum input voltage among the linear regulators. The $V_{2}$ and $V_{3}$
reach at the steady-state after $V_{1}$ reaches to the steady state. We
compute the fluctuation value of a given voltage to be 1 $\sigma$ of the
histogram made from the voltage itself. From this, we compute fluctuation
level, defined as normalized fluctuation by the mean voltage value, and for
each output voltages at steady-states are shown in Table 3, according to our
simulation results. The normalized fluctuation levels are reduced from
3.6$\times 10^{-3}$ to the order of $10^{-5}$, due to linear regulators. Note
that the maximum voltage fluctuations required by FPGA, ASICs, and optical
transceiver in the readout system is 5 $\%$, and therefore the output of the
DC to DC converter are much smaller than requirements, at least in the
simulation stage.

Figure 6:  The electric characteristics of the DC to DC converter are quantified by simulation. $V_{tps}$ is the output voltage from the TPS53318, and $V_{1}$, $V_{2}$ is fixed-output voltage from the linear regulators as 1.5 V and 3.3 V, respectively. $V_{2}$ means variable-output voltage, which tunes to 3.8 V.  Channels | Mean (V) |  $\sigma$ (V) | Fluctuation level
---|---|---|---
$V_{tps}$ | 4.95 | 1.80 $\cdot 10^{-2}$ | 3.6 $\cdot 10^{-3}$
$V_{1}$ | 1.49 | 2.18 $\cdot 10^{-5}$ | 1.4 $\cdot 10^{-5}$
$V_{2}$ | 3.29 | 2.24 $\cdot 10^{-5}$ | 6.8 $\cdot 10^{-5}$
$V_{3}$ | 3.78 | 2.22 $\cdot 10^{-5}$ | 5.8 $\cdot 10^{-5}$
Table 3:  The mean values, their fluctuations, and their normalized
fluctuations levels are shown for different voltage outputs.

###  III.2 Simulation of the stray magnetic field

As we discussed above, it is extremely important to minimize the stray
magnetic field from the DC to DC converter, and the dominant source of the
stray magnetic field is likely from the ATI. Here, the magnitude of the stray
magnetic field from the ATI is computed by our simulation. First, we assume
the maximum current of the ATI is 5 A when four ASICs and one FPGA are active.
The stray magnetic field from the ATI is simulated by COMSOL comsol . The
geometry that is used in our simulation is shown in Fig. 7 (a). Here, we use
$L_{ATI}=5.70~{}\mu$H with $r$ = 7 mm, $R$ = 8.6 mm, and $N$ = 40. The result
of our simulation is shown in Fig. 7 (b). A simulation result (closed circles)
and a fit to the result (bottom curve) are shown. A calculated inductance
value from the dipole approximation of out ATI is also shown (top curve). This
dipole approximation of the ATI can be considered as an upper limit of the
stray magnetic field. The magnitude is decreased $\propto$ $d^{-3}$, where $d$
is the distance from the center of ATI to the point of interest. Note that the
dependence of $d^{-3}$ is from the dipole radiation of the electromagnetic
field. Considering the constant 3 T magnetic field is applied in the muon
storage path, the effect from the stray magnetic field due to the ATI is
estimated to be 0.03 ppb at $d$ = 435 mm where the muon storage area is
located. We attempt to measure the magnetic field from the ATI directly using
LakeShore 425 Gauss meter Lakeshore . The non-zero stray magnetic field is
seen at the very front of the ATI. However, it is impossible to measure at a
distance where the muon storage path is located since the magnitude is too
small. However, at $d$ = 6 mm, the measured magnetic field is found to be 256
$\mu$T. From the simulation, the magnetic field at $d$ = 6 mm is about 267
$\mu$T which is somewhat larger than the measured value. This is probably from
the fact that the actual current applied is smaller than 5 A for the
measurement, or discrepancy between real coil geometry and the geometry
implemented in COMSOL.

Figure 7:  (a) The geometry of the ATI for the simulation is shown. The ATI is
drawn with Fusion 360 fusion360 , and $L_{ATI}=5.70~{}\mu$H with $r$ = 7 mm,
$R$ = 8.6 mm, and $N$ = 40. (b) A simulation result (closed circles) and a fit
to the result (bottom curve) are shown. A calculated inductance value from a
dipole approximation is also shown (top curve). The magnitude of the stray
magnetic field is obtained by COMSOL, which is represented with blue dots. A
red line means a fitting line for the results.

##  IV Fabrication and performance

Our DC to DC converter with previously discussed ATI is fabricated, and Fig. 8
shows a view of the converter. In the figure, the ATI, TPS53318 (below the
ATI), and three linear regulators can be seen. There are three output channels
to the readout electronics. Two channels produce two values of voltages (3.3 V
and 1.5 V), respectively. As a spare, the third channel is prepared for a
variable output voltage. In what follows, we study the performance of the
converter with the dummy loads to realize the environment when ASICs and FPGA
are connected to the DC to DC converter on $V_{1}$ and $V_{2}$. Two resistors
with the resistance value of 1.1 $\Omega$ are connected to 1.5 V output and
3.3 V output to generate 4.3 A as a total sum of output currents. We also
study our converter for heat dissipation.

Figure 8:  The fabricated DC to DC converter is shown. The size of the DC to
DC converter is $70\times 50~{}\rm{mm^{2}}$ and the height is $15~{}\rm{mm}$.

###  IV.1 Voltage stability

The DC to DC converter is tested to check the stability of output voltages and
the efficiency of the converter. The output voltage should be stable at
steady-state because the output from DC to DC converter will be directly
connected to electronics in the readout system. Unlike the simulation that we
discussed previously, there is extra voltage fluctuation from the internal
switching signal in the TPS53318, and it is not observed in the PSPICE
simulation. Therefore, for the real measurement, we defined the voltage
fluctuation ($\delta V$) as

$\delta V(\%)=\frac{V^{p-p}}{V^{out}}\cdot 100,$ (2)

where $V^{out}$ is the output voltage of the DC to DC converter, and $V^{p-p}$
is the peak-to-peak value of the fluctuation in $V^{out}$. We measure $\delta
V$ when the input voltage is set to 22 V. Our target value of $\delta V$ is
set to be $\leq$ 5 %. For the channel with 1.5 V output, $\delta V$ is found
to be 3.3 %, and with 3.3 V output $\delta V$ is found to be 1.7 %. Therefore,
both channels satisfy our voltage fluctuation requirement.

###  IV.2 Measurement of efficiency

The efficiency of power delivery to the readout electronics is highly related
to the chip choice of the DC to DC converter. The chip in the first stage,
TPS53318, has high efficiency of $\geq$ 90% according to the company
specification TPS53319 . However, in the case of linear regulators, the
efficiency is lower since there is a large voltage difference between the
input and output voltage in linear regulators. To study the net efficiency of
our board, we define the overall efficiency ($\eta$) as

$\eta~{}(\%)=\frac{P_{out}}{P_{in}}\cdot 100=\frac{V_{1}\cdot I_{1}+V_{2}\cdot
I_{2}}{V_{in}\cdot I_{in}}\cdot 100,$ (3)

where $I_{in}$ and $I_{out}$ are input and output currents of the DC to DC
converter. In order to check the effect from $V_{in}$ to $\eta$, we measure
$\eta$ as a function of $V_{in}$. Figure 9 shows the results of our
measurement with the dummy loads under 1 atm. The overall efficiency is found
to be $\geq$ 40 %, which is a relatively low value for a common DC to DC
converter. This is due to the fact that there are three linear regulators used
in our converter for low noise outputs. Our DC to DC converter can operate
from $V_{in}$ = 5.0 V to 25.0 V, which is slightly lager range than the
recommended range from company. There is a tendency that $\eta$ is slowly
decreased along with increasing $V_{in}$. The $P_{in}$ is measured to be 12.4
W, and the power loss $P_{loss}=P_{in}-P_{out}$ is calculated to be 7.4 W as
the maximum value when $V_{in}$ is 25.0 V. The minimum $P_{loss}$ is 6.4 W
when $V_{in}$ is 6.0 V.

Figure 9:  The measured efficiency as a function of $V_{in}$ with the dummy
loads is shown.

###  IV.3 Study of heat dissipation

The DC to DC converter will be placed in a vacuum in the real experiment.
Therefore, one has to consider the heat dissipation from the converter in that
environment. In order to study this issue, we prepare a small pseudo-vacuum
chamber as shown in Fig. 10. A small acrylic vacuum chamber with a pump is
made to study the heat dissipation from the converter to the outside. This
chamber can set a middle vacuum state ($0.015$ atm), which is similar to the
environment of the experiment. Under this environment, the temperatures at
different locations on the converter are monitored. The DC to DC converter and
temperature sensors are placed in the chamber, and the temperature values are
read. Again, $V_{in}$ is set to be 22 V with the same dummy loads used
previously.

Figure 10:  The acrylic vacuum chamber for the heat dissipation study is
shown. The radius of the chamber is 13 cm, and the height of the chamber is 20
cm with a cylindrical shape. Two plastic bars are attached to hold the DC to
DC converter in the chamber.  Figure 11:  The temperature values of the
converter as a function of time are shown. The top curve shows the temperature
for both linear regulators (overlapped), and the bottom one is for the
TPS53318.

Figure 11 shows that the temperature values of the DC to DC converter in the
chamber as a function of time. The temperature values from TPS53318 and two
linear regulators are monitored. The average temperature is about 100 ∘C for
TPS53318, and 120 ∘C for two linear regulators which is higher than the
recommended operation temperature from the company TPS53319 ; LMS1585 . We
find that our DC to DC converter works for only about 20 hours in the vacuum
chamber. After 20 hours, the board does not produce output power due to
overheating TPS53318 and linear regulators. During its operation, we find that
$P_{out}$ is 5.1 W when, therefore, $P_{loss}$ is 7.3 W. These results
indicate that an active cooling system is required to operate our DC to DC
converter in a vacuum.

##  V Conclusions

We fabricate a DC to DC converter as a low power distribution system, which
satisfies special requirements for the muon $g-2$/EDM experiment at J-PARC. We
simulate the stray magnetic field from the ATI and find that the stray
magnetic field at 0.03 ppb. The voltage stability is found to be less than 3.3
% at the measurement. Both stray magnetic field and voltage fluctuation
measurement satisfy requirements from the experiment. Finally, our study of
the heat dissipation in vacuum shows that an active cooling system is
necessary for the stable operation of the converter in the real experiment.

##  VI Acknowledgements

We would like to sincerely thank Institute for Nuclear and Particle
Astrophysics (INPA) at Seoul National University. This work is supported by a
Korea University Grant and the National Research Foundation of Korea Grant
funded by the Korean government (Grant No. NRF-2017R1A2B3007018).

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