ThG2-4
37th IEEE Power Electronics Specialists Conference / June 18 - 22, 2006, Jeju, Korea
Input Parallel-Output Series Connection of Radial Mode disk-type Piezoelectric Transformer for Thermal Balance Improvement Sangmin Lee, Sungjin Choi, Seokteak Yun, Bo H. Cho Seoul National University Department of Electrical Engineering San 56-1, Sillim-dong, Gwanak-gu, Seoul, 151-742 Email:
[email protected]
Abstract— Nowadays the Piezoelectric Transformer (PT) is used widely in power applications. However the amount of power that a PT can handle is limited and the parallel connection of PTs is needed to overcome this limit. In the parallel connection, the thermal imbalance between PTs should be prevented to avoid the thermal runaway of one of the parallel connected PTs. The mechanical resonant frequency of the radial mode disk-type PT becomes larger as the temperature increases. Because this thermal characteristic operates as the positive feedback in the conventional parallel-parallel connection, it is difficult to achieve the thermal balance. This paper introduces the parallel-series connection of the radial mode disk-type PT to improve thermal balance. The main idea is that the parallel- series connection uses the inherent thermal characteristics as the negative feedback. It is verified that the thermal balance between the PTs is improved in the proposed connection method by testing it with a constructed 40W adapter system.
I.
INTRODUCTION
The Piezoelectric Transformer (PT) may become a good alternative solution to the magnetic transformer due to a low profile and no winding. However, the power that a PT can handle is limited. In order to process the power which exceeds the PT power handling limit, the use of a multiple connected PT is needed [1-4]. For the multiple configurations of PTs, the thermal balance is important to avoid the overheating of one or more of the PTs [1]. The parallel-parallel connection reveals the thermal imbalance problem due to the mismatch of ωr and the positive temperature coefficient effect of the radial mode disk-type PT. In this paper the input parallel-output series connection is proposed to improve the thermal balance. Because the critical value of the balance is ωr, the effect of ωr in the proposed connection is analyzed in this paper. The PT used in this paper is the radial mode disk-type. The thermal balance by the proposed method is verified by a hardware experiment. The operating frequency is near the maximum gain frequency, which is higher than the resonant frequency of a PT with an
optimal load [5]. Figure 1 shows the equivalent circuit model of the PT and a detailed analysis is performed using this model. In the equations, ωs and ωr represent the switching frequency and resonant frequency of the PT, respectively. II.
PARALLEL-PARALLEL CONNECTION OF PT
Figure 2 shows the parallel-parallel connection of two PTs. The voltage across the resonant branches (Ym1, Ym2) is determined by the same input and output voltages. Thus, the resonant currents (im1, im2) can differ from each other due to the variation of the admittance of the resonant branch, as shown in (1). The variation of the admittance of the resonant branch is dominated by the resonant frequency because of the very high Q resonance of the PT, as shown in (2) [5]. Therefore the resonant frequency of each PT should be very close to each other for current sharing. This means that the thermal balance due to current sharing is very sensitive to the variation of ωr in the parallel-parallel connection. To analyze the effect of ωr, suppose that ωr is different and the other values are equal. This means that all parameters of the equivalent model are equal except Lm and Cm. These parameters are changed by the same rate to maintain C / L at a set value. m
m
V V i = (V − o1 )Y , i = (V − o 2 )Y , m1 in N m1 m2 in N m2 2 1 V =V =V o1 o 2 out
Y ≈ jω mi s
C
mi 1 L 2 Δω mi
, Δω = ωs − ωri , i = 1,2
1:N Lm
+ Vi -
Ci
Cm im Ym
Rm
+ Vp -
+ Co
Vo Fig. 2 Parallel-parallel connection of PTs
Fig. 1 The Equivalent Circuit for a Piezoelectric Transformer
1-4244-9717-7/06/$20.00
2006 IEEE.
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(1)
(2)
Thus equation (1) can be expressed as (3). i Y ( 2Y + 1/R ) m1 = m1 co L , V Den in p i Y ( 2Y + 1/R ) m2 = m2 co L V Den in p Den = (Y + Y )/N 2 + 2Y , Y = jω C p m1 m2 co co s o
(3)
In equation (3), the resonant currents of PT1 and PT2 are dominated by Ym1 and Ym2, respectively. The ratio of the magnitudes of the resonant current is calculated in (4). All equations used in the parallel-parallel connection are in the appendix. 1 1 |i |:|i | = : m1 m2 Δω Δω 1 2
(4)
As shown in (4), the relative magnitude of the resonant current is determined by ωr for a given ωs. Figure 3 shows the ratio of the resonant current magnitudes for the rising ωr2 for a fixed ωr1. The values of the parameters used in Fig. 3 are shown in Table II in the appendix. This figure means that the higher ωr causes a higher resonant current flow in the parallel-parallel connection. For a given mechanical loss factor, Rm, more current derives more loss and thus additional heat.
The material constants of the PT are dependent on the temperature. Thus, the parameter values of the PT equivalent circuit vary as the temperature of the PT [6, 7]. It is observed experimentally that the radial mode disk-type PT which is composed of PZT-4 and used in this paper, has the characteristics that ωr increases with the rising temperature. The sample is placed in a temperature chamber(DS3-2-THS, Dai-sung Engineering Co, Ltd.) which allows the sample temperature to be adjusted between 40°C and 80°C. The experimental gain curves are shown in Fig. 4. A higher ωr results in a higher resonant current, which causes more loss, and thus the temperature increases. This increased temperature further increases ωr in the parallel-parallel connection. This mechanism is similar to positive feedback and thus the mismatch of ωr makes thermal imbalance more serious in the parallel-parallel connection of the radial mode disk-type PT. III.
PARALLEL-SERIES CONNECTION OF PT
Figure 5 shows the configuration of the parallel-series connection. The voltage across the resonant branches (Ym1, Ym2) is determined by the same input voltage but by different output voltages. Thus, the resonant current (im1, im2) is determined by the variation of not only the admittance, Ym, but also by the output voltage of the PT, as shown in (5) and (6). The output voltage of each PT is different to each other and is affected by the parameters of the other PT. V V /N V V /N m1 = ( 1 − o1 1 ) , m2 = ( 1 − o 2 2 ) V V V V in in in in V Y Y /N + (Y /N − Y /N )/R o1 = o 2 m1 1 m1 1 m2 2 L , V Den in s V Y Y /N + (Y /N − Y /N )/R o 2 = o1 m2 2 m2 2 m1 1 L Den V in s Y = Y /N 2 + Y , i = 1,2 oi mi i coi Den = Y Y + (Y + Y )/R s o1 o 2 o1 o 2 L
Fig. 3 Magnitude ratio of resonant currents for ωr increase in the parallel-parallel connection
Fig. 4 The experimental gain curves of the PT with the optimal load according to the temperature
Fig. 5 Parallel-series connection of PTs
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(5)
i Y Y + (Y + Y /(N N ) + Y )/R m1 = Y co1 o 2 o2 m2 2 1 co1 L , m1 V Den in s i Y Y + (Y + Y /(N N ) + Y )/R m2 = Y co 2 o1 o1 m1 1 2 co 2 L m 2 V Den in s
|V |:|V | m1 m2 Y Y ch ch − C = −C : o o 2 2 N Δω 2 N 2 Δω 2 1
(6)
|i |:|i | m1 m2
Similar to the parallel-parallel connection case, to analyze the effect of ωr, suppose that only ωr is different and the other values are equal. Then equation (6) can be expressed as (7). i (Y /N 2 + Y )(Y + 2 /R ) m1 = Y m2 co co L , m1 V Den in s i (Y /N 2 + Y )(Y + 2 /R ) m2 = Y m1 co co L m2 V Den in s
= Y − 2 N 2C Δω :Y − 2 N 2C Δω ch o 2 ch o 1 , where Y = ch
(7)
In equation (7), the resonant current of the PT is dominated by the resonant admittance of itself and also the resonant admittance of the other PT. Thus, the resonant current is less sensitive to the mismatch of ωr in the parallel-series connection. The ratios of the voltage magnitude across the resonant branch and the resonant current magnitude are calculated in (8) and (9), respectively. All equations used in the parallel-series connection are in the appendix.
(8)
C
m1 = L m1
(9)
C
m2 L m2
Equation (8) corresponds to the fact that the relative magnitude of Vm, the voltage across the resonant branch, is determined by the resonant frequency of the other PT in the parallel-series connection. Figure 6 shows that the voltage, Vm, is inversely proportional to ωr. Because of this relation, the resonant current of the higher ωr decreases, even though Ym is proportional to ωr. The relation between ωr and the resonant current in the parallel-series connection is expressed as the equation (9). The relative magnitude of the resonant current is determined by the some constant factors, ωr and the given ωs. The effect of ωr in this ratio, is opposite to the effect in the parallel-parallel connection. Figure 7 shows the ratio of the resonant current magnitudes. The values of the parameters used in Fig. 6 and 7 are the same as the value for Fig. 3. Figure 7 shows that the higher ωr causes less resonant current to flow in the parallel-series connection. For a given mechanical loss factor, Rm, less current derives less loss and heat. Because of the thermal characteristic of the radial mode disk-type PT, less heat causes ωr to decrease. In other words, the lower ωr causes the temperature to increase and this increased temperature makes ωr higher. This means that the mismatch of ωr is relieved. Thus the direction of this mechanism is negative and the thermal imbalance due to the mismatch of ωr is improved. This implies that the parallel-series connection uses the thermal characteristics of the PT as the inherent negative feedback for the thermal balance.
Fig. 6 Magnitude ratio of Vm for ωr increase in the parallel-series connection
IV.
EXPERIMENTAL RESULTS
The parallel connection module of the PT is used in a 40W adapter prototype, which uses the Cs-Lp type topology as shown in Fig. 8 [8]. A current doubler is used as an output rectifier, and the equivalent load, Req, is π 2 RL/2, where Req is the optimal load of the PT. To operate each PT at the optimal load, the load resistance of the adapter in the parallel-parallel connection and the parallel-series connection is RL/2 and 2RL, respectively. The circuit and PT parameter values are shown in Table I. The PT used in this paper is a radial mode disk-type PT sample, made from PZT-4 ceramic. ( D.I.T. Ltd. Co.) The specifications used for the parallel connections are as follows: Fig. 7 Magnitude ratio of resonant current for ωr increase in the parallel-series connection
z
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Optimal load of the PT : 50 Ω
z z z z
TABLE I PT PARAMETER VALUES
Operating frequency : 145 kHz (max gain frequency) Cs / Lp : 30nF / 0.2mH VDC / VL (power/RL) in parallel-parallel connection : 250V / 14V (39.2W / 5Ω ) VDC / VL (power/RL) in parallel-series connection : 250V / 28V (39.2W / 20Ω )
Fig. 8 Cs-Lp type adapter using parallel connection of PT
PT1
Sample #1 Value
Sample #2 Value
Lm1
17.3mH
Lm2
18.0mH
Cm1
72.6pF
Cm2
68.9pF
Rm1
31.1Ω
Rm2
41.4 Ω
Ci1
722nF
Ci2
720nF
Co1 N1
19.9nF 0.19
Co2 N2
19.5nF 0.20
fr1
142.01kHz
fr2
142.91kHz
Figures 9 and 10 show the temperature of the PT in the parallel-parallel connection and the parallel-series connec tion, respectively. The difference of the temperatures of the two PTs is about 11.4°C when utilizing the parallel-series connection, while the difference is about 18.9°C in the parallel-parallel connection. The temperature difference in the parallel-series connection is reduced to 60% of the difference in the parallel-parallel connection. This means that the thermal balance is improved by using the parallel–series connection. V.
Fig. 9 Temperature of PT in the parallel-parallel connection
PT2
CONCLUSION
The thermal balance in the multiple connection of the radial mode disk-type PT, is improved by using the parallel-series connection. In the parallel–series connection, the sensitivity of the thermal balance to the resonant frequency is relieved. This is due to the fact that the parallel-series connection uses the thermal characteristics of the PT as the inherent negative feedback. The thermal balance in the parallel-series connection was verified using 40W adapter hardware experiments using the Cs-Lp type topology. The temperature difference in the parallel-series connection was reduced to 60% of the difference in the parallel-parallel connection. APPENDIX The equations for the parallel-parallel connection are as follows: V Y /N + Y /N o = m1 1 m2 2 V Den in p
i m1 = Y m1 V in
Y m2
i m2 = Y m2 V in
Fig. 10 Temperature of PT in the parallel-series connection
Y m1
N −N 1 1 2 +Y +Y + co1 co 2 R N N 2 L 1 2 Den p N −N 1 2 1 +Y +Y + co1 co2 R 2 N N L 2 1 Den p
(10)
(11)
(12)
The equations for the parallel-series connection are as follows:
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V Y Y /N + (Y /N − Y /N ) o1 = o 2 m1 1 m1 1 m 2 2 V Den in s V Y Y /N + (Y /N − Y /N ) o 2 = o1 m2 2 m2 2 m1 1 V Den in s
(13) (14)
Y 1 1 Y (Y + )+ (Y + m2 ) o 2 co1 R co1 N N i R m1 = Y V = Y L L 1 2 m1 m1 m1 V Den in s Y 1 1 Y (Y )+ (Y + + m1 ) o co co 1 2 2 i R R N N m2 = Y V L L 1 2 =Y m2 m2 m2 V Den in s
(15)
REFERENCES [1] [2] [3]
[4]
[5]
(16)
[6]
[7]
The parameters for Fig. 3, 6 and 7 are in table II. TABLE II PARAMETER VALUES FOR FIG. 3,6 AND 7
[8]
PT1
Value
PT2
Value
Lm1
17.3mH
Lm2
Cm1
72.6pF
Cm2
Rm1
31.1Ω
Rm2
17.1mH~ 17.3mH 71.881pF~ 72.6pF 31.1 Ω
Ci1
722nF
Ci2
722nF
Co1 N1
19.9nF 0.19
Co2 N2
19.9nF 0.19
fr1
142.01kHz
fr2
142.01kHz~ 143.43kHz
[9]
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