High-Voltage Power Supply for X-Ray Computed
Tomography and Time-Delay Compensation of CockcroftWalton Circuit
Yuki Kajiuchi1,3 and Toshihiko Noguchi2,41Canon Medical Systems Corporation, Tochigi, Japan.
Department of Engineering, Graduate School of Integrated Science and Technology,
Shizuoka University, Hamamatsu, Japan.
2

3

yuki1.kajiuchi@medical.canon

4noguchi.toshihiko@shizuoka.ac.jp

Abstract. In recent years, an image diagnostic apparatus using X-ray is intensively investigatedto reduce the radiation exposures amount. Above all, high-speed control of the high voltage
generator to control the X-ray output is a very important issue. A Cockcroft-Walton circuit (CWcircuit) is one of the method to generate the high voltage output. However, it has problem of thelong time delay in the output response due to the huge capacitive component of the CW circuit.
Therefore, it is required to achieve the stable output voltage with a quick transient response,
which can be obtained by the time delay compensation technique of the CW circuit. This paper
proposes an application of a Smith method to compensate for the time delay of the CW circuit
output to reduce the undesirable excessive radiation exposure. AS a result of verification throughthe computer simulation, it has been confirmed that the overshoot of the output voltage caneffectively be suppressed and that the optimal response can be realized without sacrificing thehigh-speed response. The paper indicates some possibilities of further improvement of the CW
circuit output response by introducing the more precise compensation technique to the X-ray
computed tomography.

1. Introduction
Declining birth-rate and aging population are advancing all over the world along with development if
medical technology and economic development. In addition, number of the patients with diseases causedby aging and lifestyle is increasing.
Image diagnostic apparatus such as X-ray computed tomography (CT) and MRI can capture organ orlike in the human body as image without giving trauma so that is indispensable of modern medical care,such as early detection and identification of various diseases. [1]
The X-ray CT system (Figure 1) is composed of scanning gantry for imaging, a bed on which the subject
is cajoled, and console operated to perform imaging. Scanning gantry is composed of rotating part andfixed part. The fixed part has interface device with the console. The rotating part has the X-ray tube thatgenerate X-ray, high voltage generator that suppling power to the X-ray tube, optical system foradjusting shape of X-ray and detector that detecting transmitted X-ray.

Figure 1. X-ray Computed Tomography
As the principle of image generation, while rotating the X-ray tube and the detector around the subject,
the subject is irradiated with X-ray and transmitted through the subject is detected by the detector. Atomogram is generated by computer that reconstruct for the difference value of the X-ray transmitted
through the object.
In recent year, following the Great East Japan Earthquake of 2011, people became interested in healtheffect of radiation exposure so image diagnostic apparatus using X-ray is required to reduce unnecessary
exposure.
2. Principle of X-ray output
The block diagram of the X-ray high voltage device is shown in figure 2 and struct of the X-ray tube isshown in figure 3. Thermionic electrons are emitted by passing electric current from the filament heating
circuit to filament in the X-ray tube. The X-ray tube is applied high voltage from High voltage power
supply to accelerate thermionic electrons. The accelerated electrons cause to collide with anode target
to generate X-ray.
The filament heating circuit controls the number of thermionic electrons (Tube current) and controls
amount of X-ray emitted from the X-ray tube. The high voltage power supply gives kinetic energy tothermionic electrons by suppling high voltage to the X-ray tube on the order of kV (Tube voltage). The
thermal electrons collide with the anode target and generate X-ray. When generate X-ray, kinetic energy
converts into X-ray intensity and transmittance. [2]Therefore, control of the tube voltage, the tube current, and the irradiation time is important to control
X-ray. In addition, the computed tomography system requires good response of output, stability of thetube voltage, reduction of output ripple.

Figure 2. Block diagram of X-ray high voltage device

Figure 3. Struct of X-ray tube
3. High voltage power supply
3.1. Conventional circuit
The conventional high voltage circuit is shown in figure 4. The rectification unit uses diodes and two
full bridge inverters using IGBT is connected in parallel to the DC bus capacitor. Inverter outputs areisolated and boosted by the transformer, and further boosted by the six-stage full-wave rectification type
Cockcroft-Walton (CW circuit). [3] The actual CW circuit is configured by connecting multiple
capacitors and diodes in series due to problem of breakdown voltage.
However, the input power factor is poor due to use of diodes in rectification unit. The CW circuit caneasily boost high voltage if number of the circuit stages are increased, but number of the elements to beconstructed increases and cost becomes higher. In addition, the conventional circuit has problem thattransient response time of the output voltage become long by increasing number of the circuit stages.
[4]

Figure 4. Conventional circuit

Figure 5. Proposed circuit
3.2. Proposed circuit
The proposed circuit is shown in figure 5. The input part is composed by PWM rectifier using
switching device to control the DC bus voltage and the input power factor. The inverter part iscomposed three full bridge inverters are connected in parallel to the DC bus capacitor and reduceenergy distribution of each inverter and the output voltage ripple are reduced by interleave operationthat pseudo raise operating frequency. The high voltage part is composed by 2 stages of half wave
rectification type CW circuits are connected in 3 series and that cause reducing number of the parts.
This paper reports on improvement of transient response in CW circuit when Smith method is applied
as delay time compensation.
4. Principle of Smith method
The Smith method is compensation method that is applied to systems with a large amount of control thedead time, and prevent excessive operations from occurring during the dead time by feedback correctionof manipulated variable a fixed time before command value.
When the consider system as show in figure 6, liner function of the system is shown in equation (1).
Here, X(s): Command value, Y(s): Output, D(s): Disturbance, Gc(s): Control function, P(s): Smith
predictor, Gp(s): System function, E(s): Dead time.
Y(s) =Gc (s)Gp (s)E(s)1+Gc

X(s) +(s){G (s)E(s)−P(s)}p{1−Gc (s)P(s)}Gp (s)E(s)1+Gc (s){Gp (s)E(s)−P(s)}

(1)

D(s)

If the Smith compensator P(s) is substitute into equation (1) as equation (2), loop transfer function
becomes equation (3).
P(s) = Gp (s){E(s) − 1}
(2)
Y(s) =Gc (s)Gp (s)E(s)1+Gc

X(s) +(s)G (s)p[1−Gc (s)Gp (s){E(s)−1}]Gp (s)E(s)1+Gc (s)Gp (s)

D(s)

(3)

Equation (3) shows that the dead time can be eliminated from denominator of transfer function between
input and output.

Figure 6. Smith Predictor Control Diagram
5. Dead time and compensation method in CW circuit
In operation of the CW circuit, capacitor is charged from lower stage to upper stage each time polarityof applied voltage is reversed. In case of circuit shown in figure 7, the output voltage is obtained by sumof potential differences of even stages capacitors. Therefore, the output voltage is determined by sum ofcharges supplied for number of stages of the CW circuit in operation cycle.
Formulate dead time E(s) in equation (4). Here, n: Half number of the CW circuit stages, Lp: Powersupply operating cycle.
1E(s) = n (e−Lps + e−2Lp s + e−3Lps + ⋯ + e−nLp s )(4)
The inverter output voltage that proportional to manipulated variable, so it can be considered as unity
gain. When considering the voltage amplification factor K, the system function will be Gp (s) = K andas shown in equation (5).
Gp (s)E(s) = 2(e−Lp s + e−2Lps + e−3Lp s + ⋯ + e−nLps )(5)
The Smith predictor P(s) is shown in equation (6) by substituting each value into equation (2).
P(s) = 2(e−Lps + e−2Lp s + e−3Lps + ⋯ + e−nLp s ) − K
Figure 8 shows the block diagram of the control system in time domain.

Figure 7. CW circuit output voltage delay

Figure 8. Control diagram with Smith predictor(6)Figure 9. Diode simulation model
6. Simulation
6.1. Diode model
In case of the CW circuit is composed of ideal capacitor and ideal diode, it is difficult to simulate.
Because charge and discharge time constant between capacitors become zero. [5] Therefore, inconsideration of influence of junction capacitance of diode for output voltage of the CW circuit, thesimulation was performed using model that incorporates junction capacitance in ideal diode.
The diode model used for simulation is shown in figure 9. Here, 𝑉𝑓 : Forward voltage drop, 𝑅𝑓 : Forward
resistance, 𝐶𝑗 : Junction capacitance，𝑅𝑑 : Discharge resistance，𝑅𝑐 : Charge resistance，𝑅𝑟 : Reverse
resistance.
6.2. Simulation results
The simulation was performed on assumption that the 12-stage CW circuit is driven by full bridge
inverter like figure 10 using simulation application PSIM. The simulation values are shown in table 1.
The load resistance RL was set that the output current was 600mA. Simulation results are shown infigure.11. (A) is result of applying the conventional Smith method in TD = 0.0008. (B) is result ofapplying the conventional Smith method in TD = 0.0014. (C) is result of applying the proposed Smith
method in TD = 0.00005. TD indicates delay time.
Even if the proposed method is not applied, overshoot can be suppressed by increasing time delay, but
the output voltage waveform is distorted because the change of command value becomes discontinuous.
On the other hand, when the proposed method is applied, the response can be made close to the firstorder delay while suppressing overshoot of output voltage waveform. However, even if the proposed
method is applied, overshoot remains in output voltage waveform, so it is difficult to realize perfectfirst-order response.
Parameter
Capacitor Ccw1~12
Turn ratio Np:Ns
Output voltage
command value

Table 1. Simulation parameters
Value
Parameter
100 nF
DC voltage Vdc
1:40
Proportional gain Kp
Integration time
120 kVTiconstantsValue360V
0.20.0005

Figure 10. Simulation circuit(A) Conventional Smith (TD=0.0008)(B) Conventional Smith (TD=0.0014)(C) Proposed 6-times Smith (TD=0.00005)
Figure 11. Output voltage waveform7. Conclusions
In this study, proposed applying the Smith compensation method to the CW circuit and confirmed theeffect by simulation. When the time delay element is one, the output voltage waveform is distorted by
the output voltage command value changes discontinuously but overshoot of the output voltage
waveform can be suppressed and output response can approach primary delay system by increasing timedelay element according to number of the stages of CW circuit.
However, overshoot of the output voltage waveform remains with apply the proposed method andperfect primary delay response has not been achieved. In the future, consider more rigorouscompensation using the proposed method and we aim to improve output response of output voltage
further.
References[1] S Takase, Y Akiyama, and N Mizutani 2005 Trend of diagonostic imaging equipment in recent
years Journal of Institute of Electrical Equipment Engineer, Vol.25, No.5, PP.313-316.
[2] Y Katsube 2015 The Elements and Design of X-Ray Generator Adv. X-ray. Chem. Anal., Japan46, pp.27-31.
[3] S Miyazaki 2000 Radiology and Characteristics of Inverter Type X-ray Generator, Journal ofJapanese society of Radiation Technology, Vol.56, No.1, PP.22-42.
[4] Yoshio Takamura 1986 Analysis of a Cockcroft-Walton circuit by a newly developed graphicalmethod Denki Gakkai Ronbunshi, Vol.106C, No.7, PP.119-126.
[5] Masataka Minami, Takeshi Ito, Shin-ichi Motegi and Masakazu Michihira 2016 Boost Ratio andPower Factor Improvement in Cockcroft-Walton Circuit with Diode Junction Capacitor, IEEJ
Transactions on Industry Applications, Vol.136, No.12, PP.991-996.