Switchless compact dual-band matching networks for class-E power amplifiers

Abstract

Two compact switchless dual-band load networks for class-E power amplifier (PA) operating at 800 and 1900 MHz are proposed, featuring small area and low loss which will be suitable for non-concurrent dual-band PA module in handset. Theoretical analysis and design equations are provided along with a loss model, including loss in the transistor and in the load network. Loss model is extracted for each structure to find the design parameters for optimized and balanced efficiency in both bands. Both designs are fabricated on Rogers RO4003 substrate with lumped components. Full PA simulations of both bands are carried out with co-simulation using a Triquint TGF2023-2-10 GaN transistor model, lumped components and EM models of load network layouts for both structures. The PA with transformer-based load network achieves a power added efficiency of 68.6 % at low band and 62.6 % at high band at an output power of 37.8 and 36.7 dBm respectively. The overall area consumed by the load network is 13.5 × 9.6 mm². The LC-based PA has a similar PAE of 68.3 and 60 % at low band and high band, respectively. The output power is 38.1 dBm in the low band and 37 dBm in the high-band. The overall area consumed by the load network is 9 × 10 mm²

Appendices

Appendix 1: Derivation of effective inductance for LC-based load network

Referring to Fig. 2, the effective impedance of the combination of $L_{1}$, $L_{2}$, and $C_{2}$ is inductive at both $\omega_{L}$ (denoted $L_{eff,L}$) and $\omega_{H}$ (denoted $L_{eff,H}$). For the low-band we can write:

$$j\omega_{L} L_{eff,L } = j\omega_{L} L_{1} + \left( {j\omega_{L} L_{2} \parallel \frac{1}{{j\omega_{L} C_{2} }}} \right) = j\omega_{L} L_{1} + \left( {\frac{1}{{j\omega_{L} L_{2} }} + j\omega_{L} C_{2} } \right)^{ - 1}$$

(19)

which can be written as:

$$j\omega_{L} L_{eff,L } = j\omega_{L} L_{1} + \frac{{j\omega_{L} L_{2} }}{{1 - \omega_{L}^{2} L_{2} C_{2} }}$$

(20)

previously we defined: $\omega_{2} = 1/\sqrt {L_{2} C_{2} }$ and using this definition we can write:

$$j\omega_{L} L_{eff,L } = j\omega_{L} L_{1} + \frac{{j\omega_{l} L_{2} }}{{1 - \omega_{L}^{2} /\omega_{2}^{2} }} .$$

(21)

Finally, (21) can be written in the form of (5) as:

$$j\omega_{L} L_{eff,L } = j\left( {\omega_{L} L_{1} - \omega_{2} L_{2} \frac{{\omega_{L} \omega_{2} }}{{\omega_{L}^{2} - \omega_{2}^{2} }}} \right) .$$

(22)

The same derivation is used for (6) just substituting $\omega_{H}$ for $\omega_{L}$.

Appendix 2: Derivation of effective impedance and harmonic impedance for transformer-based load network

The derivation of (9) is based on the model shown in Fig. 18 where $R_{2}$ represents the parasitic resistance of $L_{2}$. The port voltages $V_{1}$ and $V_{2}$ can be related to the currents $I_{1}$ and $I_{2}$ by the following equations:

$$V_{1} = j\omega L_{1} I_{1} + j\omega MI_{2}$$

(23a)

$$V_{2} = j\omega L_{2} I_{2} + j\omega MI_{1}$$

(23b)

$$V_{2} = - \frac{{I_{2} }}{{j\omega C_{2} }} - R_{2} I_{2}$$

(23c)

where $M$ is the mutual inductance between the primary and secondary windings. From (23b) and (23c) we can write:

$$I_{2} = \frac{\omega M}{{\frac{1}{{\omega C_{2} }} - \omega L_{2} + jR_{2} }}I_{1} .$$

(24)

Fig. 18

Transformer model used in the derivation of (9)

By substituting (24) into (23a), the effective impedance of the transformer can be written as:

$$\begin{aligned} Z_{eff} &= \frac{{V_{1} }}{{I_{1} }} = j\omega L_{1} + j\frac{{\left( {\omega M} \right)^{2} }}{{\frac{1}{{\omega C_{2} }} - \omega L_{2} + jR_{2} }} \\ &= j\omega L_{1} + j\frac{{\omega^{2} k^{2} L_{1} L_{2} }}{{\sqrt {\frac{{L_{2} }}{{C_{2} }}} \left( {\frac{1}{{\omega \sqrt {L_{2} C_{2} } }} - \omega \sqrt {L_{2} C_{2} } } \right) + jR_{2} }}\\ &= j\omega L_{1} + j\frac{{\omega^{2} k^{2} L_{1} \frac{1}{{\omega_{2} }}}}{{\left( {\frac{{\omega_{2} }}{\omega } - \frac{\omega }{{\omega_{2} }}} \right) + jR_{2} \sqrt {\frac{{C_{2} }}{{L_{2} }}} }}\\ &= j\omega L_{1} \left[ {1 + \frac{{k^{2} \frac{\omega }{{\omega_{2} }}}}{{\left( {\frac{{\omega_{2} }}{\omega } - \frac{\omega }{{\omega_{2} }}} \right) + jR_{2} \frac{1}{{\omega_{2} L_{2} }}}}} \right]\\ &= j\omega L_{1} \left[ {1 + \frac{{k^{2} \alpha }}{{\left( {\frac{1}{\alpha } - \alpha } \right) + j\frac{1}{{Q_{T} }}}}} \right]\\ &= j\omega L_{1} \left[ {1 + \frac{{k^{2} \left( {1 - \alpha^{2} } \right)}}{{\left( {\frac{1}{\alpha } - \alpha } \right)^{2} + \frac{1}{{Q_{T}^{2} }}}} - j\frac{{k^{2} \alpha /Q_{T} }}{{\left( {\frac{1}{\alpha } - \alpha } \right)^{2} + \frac{1}{{Q_{T}^{2} }}}}} \right]\\ &= \omega L_{1} \frac{{k^{2} \alpha /Q_{T} }}{{\left( {\frac{1}{\alpha } - \alpha } \right)^{2} + \frac{1}{{Q_{T}^{2} }}}} + j\omega L_{1} \left[ {1 + \frac{{k^{2} \left( {1 - \alpha^{2} } \right)}}{{\left( {\frac{1}{\alpha } - \alpha } \right)^{2} + \frac{1}{{Q_{T}^{2} }}}}} \right] \end{aligned}$$

(25)

where $\alpha_{(L,H)} = \omega_{{\left( {L,H} \right)}} /\omega_{2}$, $k$ is the coupling coefficient, and $Q_{T} = \omega_{2} L_{2} /R_{2}$ is the quality factor of the secondary winding with $\omega_{2} = 1/\sqrt {L_{2} C_{2} }$.

Finally, the harmonic impedance of the transformer-based load network is given in Eqs. (18a) and (18b) which express the magnitude of the 2nd-harmonic impedance and the 3rd-harmonic impedance, respectively, for both bands. The total impedance of transformer-based dual-band load network (Fig. 4) as a function of angular frequency ($\omega$) can be expressed as:

$$Z_{L} \left( \omega \right) = Z_{eff} + j\omega L_{S} + \frac{1}{{j\omega \left( {C_{o} + C_{S} } \right)}} + j\omega L_{P} ||\frac{1}{{j\omega C_{P} }}||50$$

(26)

which can be expanded to the form:

$$Z_{L} \left( \omega \right) = j\omega L_{1} \left( {1 + \frac{{k^{2} \alpha (\omega )}}{{\frac{1}{\alpha (\omega )} - \alpha (\omega )}}} \right) + \frac{{\omega L_{1} {\text{k}}^{2} }}{{\left( {\frac{1}{\alpha (\omega )} - \alpha (\omega )} \right)^{2} }}{ \cdot }\frac{\alpha (\omega )}{{Q_{TX,L\left( H \right)} }} + j\omega L_{S} + \frac{1}{{j\omega \left( {C_{o} + C_{S} } \right)}} + j\omega L_{P} ||\frac{1}{{j\omega C_{P} }}||50 .$$

(27)

which has the same form as (18a) and (18b).