1

Wireless Power Transfer Using Resonant Inductive Coupling for 3D Integrated ICs

Sangwook Han, and David D. Wentzloff

Electrical Engineering and Computer Science Department The University of Michigan, Ann Arbor

swhanpns, wentzlof@umich.edu

Abstract- In this paper we introduce a wireless power transfer

scheme using resonant inductive coupling for 3DICs to enhance power transfer efficiency and power transfer density with smaller coils. Numerical analysis and optimal conditions are presented for both power transfer efficiency and density. HFSS simulation results are shown to verify the theoretical results. Coils for the power link are designed using a Chartered 0.13µm CMOS process. The peak power transfer efficiency is 52% and power transfer density is 49mW/mm2.

I. INTRODUCTION

3D integration is a promising solution for shortening interconnect in parallel processing in order to achieve smaller form-factor and higher performance. Several wired and wireless methods have been proposed to implement data communication among vertically stacked ICs in a package [1,2]. However, only wired methods such as wire-bonding or micro-bumps have been used for the power supply, even though wireless power delivery has unique advantages in 3DIC applications. It can eliminate the Known-Good-Die (KGD) issues to improve the yield, and some MEMS applications require non-contact power transfer [3], which can be realized by wireless power transfer. Fig. 1 illustrates two examples of systems requiring wireless power transfer.

Previous work has reported wireless power transmission between two inductively coupled coils in stacked dies within a package [4]. This uses standard inductive coupling which results in relatively low power efficiency (<30%) and large coils (700x700µm) since most of flux is not linked between the coils. The resonance of an inductively coupled system increases the amount of magnetic flux linked between coils and improves the power transmission significantly [5]. In this paper, we will introduce wireless power transfer using resonant inductive coupling for 3DICs to increase power transfer efficiency and density with smaller coils.

The paper is organized as follows; In Section II, we will discuss power transfer efficiency. The optimal condition and numerical analysis on maximum power transfer efficiency will be introduced. Section III discusses power transfer density. In IC designs, silicon area is always a major concern. Therefore, power density is sometimes more critical than power efficiency inside a package. We will discuss the optimal values for coil size, load resistance, and coupling coefficient k for maximum

power transfer density. Section IV will show the coil design for an inductive power link and the simulation results of power efficiency and density. Section V concludes the paper.

II. POWER TRANSFER EFFICIENCY

A. Equivalent Circuit Fig. 2 shows the concept of an inductive power link and its

equivalent circuit. The RF input signal with a power amplifier in the transmitter is modeled as a voltage source in the primary resonator. The receiver is modeled as a resister RL in the secondary resonator. k is the transformer coupling coefficient, and L1 and L2 are self-inductance in transmitter and receiver coils, respectively. R1 and R2 model the losses in the coils. C1 and C2 are capacitors including parasitic and external capacitance to create a resonance at the transmitter and receiver side. Standard inductive coupling uses a frequency well below the self-resonant frequency of the inductors, therefore parasitic

Fig. 1. The applications of wireless power transfer using inductive coupling:(a) Vertical stacking of heterogeneous processes such as logic and DRAM(b) Information Tethered Micro Automated Rotary Stages (ITMARS).Sensors and communication link are integrated on a rotating stage in asubstrate.

2

capacitance (C1, C2) are typically ignored in this case. Resonant inductive coupling, however, uses this capacitance to resonate with the inductors, increasing the flux linked between transmitter and receiver.

B. Analysis with Equivalent Circuit As shown in Fig. 3 (a), the circuit with a transformer can be

converted to the equivalent circuit with the reflected load Ze. Ze captures the impact of the secondary part on the primary part. The reflected impedance Ze can be expressed by

′ ′

′ (1)

where / / ‖ . The power consumed at Ze should be identical to the power transferred to the secondary part. Considering that the real part of (1) is the resistive component, we can derive the fraction of delivered power to secondary part at resonance. This is the power efficiency at the primary side, η1.

′

′ (2)

At the secondary equivalent circuit, shown in Fig. 3 (b), the

parasitic resistance can be converted into an equivalent parallel loss across the LC tank. The power from the primary part will be dissipated in both R2 and RL, and the power consumed at RL represents the net output power available at the receiver. At resonance, the power efficiency at the secondary part, η2 can be written as

(3)

Combining (2) and (3), the total power efficiency of the inductive power link is derived as a form similar to [6-8].

′

′∙ (4)

C. Maximum Power Transfer Efficiency The power transfer efficiency can be maximized by adjusting

conditions such as R, L, C of coils and RL value. In practice, for planar integrated spiral inductors it is difficult to adjust the L, C, and R values of the coils independently, since all the values are partially correlated. Therefore, RL is the best practical factor to adjust when optimizing the wireless link for a given coil. By differentiating (4) w.r.t. RL, the optimal RL can be obtained as

(5)

This optimal condition makes the maximum power transfer

efficiency a function of coupling coefficient k and quality factor of the coils, both of which may be optimized when designing the coils.

(6)

With large values of k and Q, the power efficiency approaches 1 as expected.

III. POWER TRANSFER DENSITY

While high power transfer efficiency is critical for low power systems, area-constrained systems can require larger power transfer through smaller area coils at an acceptable loss in efficiency. With a fixed distance between two coils, larger coils result in larger k and higher efficiency. However, using larger coils requires more silicon area, and it ultimately decreases the power transfer density. Therefore, a parallel power transfer scheme can be taken into consideration in order to increase power density and maximize the amount of power delivery through the same area, as illustrated in Fig. 4.

Fig. 2. (a) Concept of wireless inductive power link (b) Equivalent circuit

Fig. 3. (a) Entire equivalent circuit (b) Secondary equivalent circuit

3

Fig. 5. Equivalent circuit for power density calculation

In order to compare the performance of single inductive power link to a parallel inductive power link, the power transfer density should be analyzed first.

A. Output Delivered Power Fig. 5 shows that the transformer circuit has the equivalent

circuit with reflected impedance and parallel resistance. The reflected impedance is split into the imaginary and real part, and the real resistive part is converted to parallel resistance using quality factor / .

At resonance, the input power is given by

| |

(7)

and the output power can be written as

∙ ∙ ∙| |

∙ ∙| |

(8)

B. Optimal Load The power transfer also can be maximized by adjusting the

RL value. By differentiating (8) w.r.t. RL at resonance, the optimal RL can be expressed as

1 (9) Substituting the optimal RL into (8), we get the maximum

power transfer amount as

| | (10)

C. Power Transfer Density The power transfer density is defined as the amount of

available transferred power per the unit area. Assuming square-shaped, planar spiral coils are used with diameter d, the power transfer density will be a function of d. In addition, coupling coefficient k is also the function of d [9].

.

(11)

where x is the distance between coils. With (11), the power transfer density is given by

| |

| |

∙ (12)

By differentiating (10) w.r.t. d, the optimal size of the coils and corresponding k can be found as the function of the separation between coils, x. For instance, when x=15μm, the optimal d is 58μm, and k is equal to 0.41.

IV. SIMULATION RESULTS

A. Simulation Setup To verify this model, we designed planar spiral coils using a

Chartered 0.13µm CMOS process. Fig. 6 shows the simulation setup of two identical square coils vertically stacked to implement the inductive power link through stacked ICs. We sweep the separation x, and the diameter d to test power efficiency and density. HFSS is used to extract the lumped-element models for coils, and these models are imported to Sperctre to simulate the inductive power link.

B. Power Transfer Efficiency As shown in (6), the maximum power transfer efficiency

strongly depends on k. To show this dependency, we swept the

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Sangwook Hholarship. Thculty Award.

K. Niitsu, Y. Nonomura, MHasegawa, anIntegration of ISSCC Dig. TecR. Cardu, M. Sand R. GuerriCoupling,” IEEInformation TDARPR MTO http://www.darK. Onizuka, H“Chip-to-Chip Applications,” A. Kurs, A. KSolijacic, “WiResonances,” SW. H. Ko, S. PPowered Coils 15, pp. 634-640M. W. Baker aPower Links fCircuits Syst. VU. Jow and MCoils for EfficiTrans. Biomed.N. Miura, D. Design of InduChip Wireless 40, pp.829-837

results: power trdensity of three ca

Total Am0.0

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ACKNOW

Han is partis work is su

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