Load-pull Simulation for Wideband Operation

After determining the device size and the bias condition, performing load-pull simulation is the next step to find the optimal load impedance (Zopt). Since wide bandwidth with high output power is required for this PA, the load-pull simulation over 24 to 43 GHz is required. However, the PA cell needs to accomplish the transistor combiner EM simulation. Then do the load-pull simulation. Otherwise, the result will be inaccurate. Fig. 3.7 and Fig. 3.8 show the load-pull simulation results of the power stage cells at 28 GHz, 34 GHz and 38 GHz, including Zopt, input impedance, PAE and Psat. The simulation result shows the real parts of Zopt and Zin are only around 10 and 4 Ω, respectively, at 28 GHz and 38 GHz. The Psat and PAEMAX are around 25 dBm and 40%. The Zopt consists a constant resistance in parallel with an equivalent negative capacitance across a wide bandwidth. When the size of the device increases, the output current swing will increase proportionally, then leads to higher output power. In the meanwhile, the negative capacitance will be decreased proportionally, which causes a lower imaginary part of the optimal impedance. Hence, as shown in the Fig. 3.9, the traces of Zopt of PAE and Pout on the Smith chart became closer. The comparison shown in the Fig. 3.9 is the device size of this work compared with half the device of this work. The device size of cascode cell is 4 × 3 µm × 32 fingers at common-gate stage and 4 × 3.5 µm × 32 fingers at common-source stage.

Fig. 3.7 Load-pull simulations of the power stage cells at 28 GHz.

Fig. 3.8 Load-pull simulations of the power stage cells at 38 GHz.

0.2 0.5 1.0 2.0 5.0 0.2j

0.5j

1.0j

2.0j

PAE 5.0j

P _out

PAE P _out

Half the device size of this work

Fig. 3.9 Simulated optimal impedance on smith chart from 24 to 43 GHz.

3.2.5 The Proposed Broadband Matching Network

Recently, transformer-based matching techniques have been wildly used in PAs.

Transformers are attractive in the wideband circuits design because they can provide a high-order LC network with almost the same chip area as a single inductor and for isolating dc current from two components while maintaining ac continuity. Essentially, a transformer consists of two winding inductors linked by the mutual magnetic field. When the primary coil applied an ac current, a varying flux is generated. The amplitude of the flux is dependent on the applied voltage and number of turns in the winding. Mutual flux linked to the secondary coil induces a voltage whose amplitude depends on the number of turns in the secondary winding. Mutual coupling is accomplished simply with air. More effective flux linkage is obtained with the use of a core of iron or ferromagnetic material with a higher permeability than that of air. The magnetic coupling coefficient k is to specify the relation between a certain orientation of inductors with arbitrary inductance as

p s

k M

= L L (3.6)

where M denotes the mutual inductance between two coils, LP denotes the self-inductance of the primary coil, and LS denotes the self-inductance of the secondary coil. The range of k is between 0 and 1. However, the range of k can also be defined between -1 and 1, which allowing a negative k to represent the phase inversion of the coil and the windings.

Fig. 3.10 shows the schematic of proposed matching network which contains the transformers, two parasitic capacitances, and the load impedance. Two resonant frequencies fH and fL of the transformers (fH > fL) can be expressed as [18]

^{L 2} P

(

)

(

)

f = π L k C = π L k C

+ + (3.7)

(

) (

)

2 1 2 1

H

P O S PAD

f = π L k C = π L k C

− − (3.8)

By dividing the (3.7) and (3.8), fH can be expressed as

L

1+

H 1 f f k

= k

− (3.9) From (3.9), k needs to be designed as large as possible to synthesize the required impedance. When k is increased, fH become higher. Theoretically, when k approach unity, f^H approach to infinity. This effect is clearly shown in Fig. 3.11. The peak load impedance at the fH is greatly reduced, and a small variation of load impedance versus frequency can be obtained. In other words, a low k is not possible to realize the required impedance transformation. As shown in Fig. 3.12, a higher k results in a larger induced current, leading to a lower passive loss. As stated above, the secondary coil of the transformers needs to overlap the primary coil as much as possible for better coupling. Therefore, the optimum impedance can be obtained with the broadband matching network without extra lumped elements, which may cause additional passive loss. This helps the PA to achieve better output power bandwidth performance.

k L P Ls

C O C PAD

R _O R L

Fig. 3.10 The schematic of transformer-based matching network

Fig. 3.11 Simulated the transformer impedance with different magnetic coupling coefficient k.

Fig. 3.12 Simulated insertion loss versus magnetic coupling coefficient at different frequency.

In the design of a broadband matching network, the impedances need to be transformed to the optimal impedances of the power cells. However, as shown in Fig.

3.13, in an even two-way current combiner, each of the transformers need to match the impedance from Zin/Zopt to 2 × Z^L. The real part of Zopt and Zin are around 10 and 4 Ω, respectively, at 24 to 43 GHz which are much lower than 2 × Z^L, leading to a very high impedance transformation ratio, and therefore difficult to implement. In order to alleviate this problem, a slotted low impedance transmission line and the parasitic shunt capacitance of the RF signal pad (CPAD = 30 fF) are utilized to lower the magnitude of 2 × ZL from 100 to 80 Ω at 34 GHz. As shown in Fig. 3.14. By selecting 20-Ω characteristic impedance and 50 µm low-impedance transmission line, respectively, the differential load impedance variation of the output transformer is flattened across a wide bandwidth.

Reducing the load impedance not only decreases 0.2-dB insertion loss of transformers, but also achieves a higher k of the transformers more easily, and then leads to the broadband performance. Fig. 3.15 shows the detail of proposed matching network. The matching network composes of a 1:2 transformers with 0.9 k and a 1:3 transformers with 0.8 k. From (3.9), the theoretical fH of the input and output transformers are 19 and 3 (= 9) times higher than fL, respectively. As shown in the Fig. 3.16, the simulated fH is 3 to 4 times higher than fL which agrees with the theory. The simulated impedances between two resonant frequencies are almost the same. The simulated insertion loss of the matching network at 34 GHz is only 1.2 dB at the output and 1.8 dB at the input. As shown in Fig. 3.17, when Zopt and Zin match to the impedance of transformers, the return loss is better than 10 dB across a wider bandwidth. The results verify the matching network broadband matching characteristics.

Fig. 3.13 The EM layout of low-impedance transmission line.

Fig. 3.14 The simulated impedance of output transformers at different load impedance ZL.

VG,PA VD,PA

Fig. 3.15 The setup for checking the return loss of the matching network.

0 20 40 60 80 100 120 Fig. 3.16 The simulated impedance versus frequency.

20 25 30 35 40 45 50

However, because of the high output power, the proposed PA possesses a large voltage swing which then facilitates the electric field of transformers. Hence, the shield topology is adopted to diminish the substrate current by preventing the electric field leaking to the substrate [50]. Fig. 3.18 shows the EM layout of transformers with three different shield topologies. Fig. 3.19 shows the simulated maximum gain with different shield topology. As the result, the maximum gain of transformer with floating shield are higher than another topology. Hence, floating shield is selected to mitigate the insertion loss. By applying the shield to the transformers, the Q-factor is increased by 20% while the inductance is barely affected.

(a) (b) (c) Fig. 3.18 The layout of (a) no shield (b) floating shield (c) patterned ground shield.

20 25 30 35 40 45 50

-2.5 -2.0 -1.5 -1.0 -0.5

patterned ground shield floating shield

no shield

M axmi um G ai n (d B)

Frequency (GHz)

Fig. 3.19 Simulated maximum gain of transformer with different shield topology.

As shown in Fig. 3.20, the small-signal conjugate matching impedance is different from the Zopt, and the matching network is not possible to match to both impedances simultaneously. In order to achieve a wider bandwidth of the Psat, this work focuses on the broadband power matching. Hence, the small-signal gain variation is not as small as the output power variation across the frequency range.

0.2 0.5 1.0 2.0 5.0 0.2j

0.5j

1.0j

2.0j

5.0j

S

P _out ^PAE

(a)

0.2 0.5 1.0 2.0 5.0 0.2j

0.5j

1.0j

2.0j

5.0j

S

Z

(b)

Fig. 3.20 The simulated Zopt and small-signal conjugate matching impedance on Smith chart from 24 to 43 GHz at (a) output and (b) input matching network.