2.2.1 Doherty Amplifier Operation With Knee Voltage

Theoretically, the Doherty amplifier has the highest efficiency at the 6 dB back-off and the peak power levels. The maximum efficiencies at the two power points can be achieved through the perfect load modulation of the carrier and peaking amplifiers. The perfect load modulation of the carrier amplifier with a zero knee voltage, depicted in Fig. 2.11A, indicates that the output powers for both R_OPT^Ideal and 2R_OPT^Ideal are P₁^Ideal and P₁^Ideal/2, respectively. The efficiencies (η^Ideal's) are also the same at the two power levels; the carrier amplifier is in equally saturated states for the both cases. In this operation, P₁^Ideal, η^Ideal, and R_OPT^Ideal are given by

$P_1^{\text{Ideal}}=\frac{1}{2}\bullet I_{1,C}\left({\theta }_C\right)\bullet V_1$

${\eta }^{\text{Ideal}}=\frac{P_1^{\text{Ideal}}}{P_{\mathit{dc}}^{\text{Ideal}}}\times 100=\frac{\left(1/2\right)\bullet I_{1,C}\left({\theta }_c\right)}{I_{\mathit{dc},C}\left({\theta }_c\right)}\times 100$

$R_{\mathrm{OPT}}^{\text{Ideal}}=\frac{V_1}{I_{1,c}\left({\theta }_c\right)}$

where

$I_{1,C}\left({\theta }_c\right)=\frac{I_{\max }}{2\pi }\bullet \frac{{\theta }_c-sin{\theta }_c}{1-cos\left({\theta }_c/2\right)}$

$I_{\mathit{dc},C}\left({\theta }_c\right)=\frac{I_{\max }}{2\pi }\bullet \frac{2\bullet sin\left({\theta }_c/2\right)-{\theta }_{c}cos\left({\theta }_c/2\right)}{1-cos\left({\theta }_c/2\right)}$

I_1,C(θ_C) and I_dc,C(θ_C) are the fundamental and dc current components, respectively, of the carrier amplifier biased at the conduction angle θ_c. In the ideal case, V₁ is equal to V_dc because of the zero on-resistance with zero knee voltage.

In a real device, the effect of the knee voltage should be considered. Fig. 2.11B shows a load line with the knee voltage V_k. For R_OPT and 2R_OPT, the load impedances are given by

$R_{\mathrm{OPT}}=\frac{V_{\mathit{dc}}-V_k}{I_{1,c}\left(\mathit{\theta c}\right)}$

$R^{\text{Case}\_\mathrm{I}}=2R_{\mathrm{OPT}}=\frac{V_{\mathit{dc}}-V_k^{\prime }}{i_{1,c}^{\prime }\left({\theta }_c\right)}$

where

$i_{1,c}^{\prime }\left({\theta }_c\right)=\frac{i_{\mathit{max}}^{\prime }}{2\pi }\bullet \frac{{\theta }_c-sin{\theta }_c}{1-cos\left({\theta }_c/2\right)}$

$V_k=R_{\mathrm{on}}\bullet I_{\max }$

$V_k^{\prime }=R_{\mathrm{on}}\bullet i_{\max }^{\prime }$

In Case I with 2R_OPT, i′_max can be derived from the loadlines in Fig. 2.11

$i_{\max }^{\prime }=\frac{I_{\max }{V}_{\mathit{dc}}}{2V_{\mathit{dc}}-I_{\max }{R}_{\mathrm{on}}}$

i′_max represents the maximum current when the carrier amplifier has the load impedance of 2R_OPT. Thus, the output powers for the R_OPT and R^Case_I cases can be calculated as follows:

$P_{R_{\mathrm{OPT}}}=\left(\frac{1}{2}\right)\bullet I_{1,c}\left({\theta }_c\right)\bullet \left(V_{\mathit{dc}}-V_k\right)$

$P^{\text{Case}\_\mathrm{I}}=\left(\frac{1}{2}\right)\bullet i_{1,c}^{\prime }\left({\theta }_c\right)\bullet \left(V_{\mathit{dc}}-V_k^{\prime }\right)$

The powers are plotted in Fig. 2.12A. For the calculation, it is assumed that V_dc is 30 V and I_max is 8 A with uniform transconductance. θ_c is fixed at 210°. As shown, the carrier amplifier with 2R_OPT delivers the power more than a half of P_ROPT because of the enlarged voltage and current swings from (V_dc − V_k) to (V_dc − V_k′) and from I_max/2 to i′_max, respectively. The efficiency at the 6 dB back-off region does not reach to the peak value because the carrier amplifier, which is optimally designed for R_OPT load, is not in the saturation state when the peaking amplifier is turned on.

To maximize the efficiency at the 6 dB back-off power region, the carrier amplifier with nonzero knee voltage should have a load impedance larger than 2R_OPT, like Case II in Fig. 2.11B. As shown, the current is reduced, but the voltage swing is increased, maintaining the 3 dB lower power. In this case, the output power can be written as

$P^{\text{Case}\_\mathrm{II}}=\left(\frac{1}{2}\right)\bullet i_{1,c}^{″}\left({\theta }_c\right)\bullet \left(V_{\mathit{dc}}-V_k^{″}\right)$

where

$i_{1,c}^{″}\left({\theta }_c\right)=\frac{i_{\max }^{″}}{2\pi }\bullet \frac{{\theta }_c-sin{\theta }_c}{1-cos\left(\frac{{\theta }_c}{2}\right)}$

$V_k^{″}=R_{\mathrm{on}}\bullet i_{\max }^{″}$

Since P^Case-II should be half of P_ROPT, i″_max, the maximum current when the carrier amplifier has a load impedance larger than 2R_OPT, can be calculated:

$i_{\max }^{″}=\frac{1}{R_{\mathrm{on}}}\bullet \frac{V_{\mathit{dc}}-\sqrt{{\left(V_{\mathit{dc}}\right)}^2-2\bullet V_k\bullet \left(V_{\mathit{dc}}-V_k\right)}}{2}$

As shown in Fig. 2.12A, the maximum output power is decreased with R_on. But P^Case_I does not change much since i′_max is increased and the knee voltage is reduced. Therefore, the difference from P_ROPT is smaller than 3 dB. Fig. 2.12B shows the required load impedance for various R_on. As R_on increases, the load impedance of the carrier amplifier in the low-power region also increases, larger than 2R_OPT.

To verify the knee voltage effects on the Doherty operation, the carrier amplifier is designed and tested using a Cree GaN HEMTCGH40045 device with a 45 W power at 2.655 GHz. First, the output of the amplifier is matched to 50 Ω. Its load impedance is then modulated by adjusting the offset line and output termination impedance. Fig. 2.13 shows the load modulation results for the carrier amplifier employing the output termination impedances of 50, 100, and 130 Ω. As expected, the PA with 100 Ω delivers maximum efficiency at 45.3 dBm, which is 1.9 dB back-off power from the maximum output power of 47.2 dBm with R_OPT of 50 Ω. On the other hand, the PA with 130 Ω has its maximum efficiency at the 2.9 dB back-off power.

2.2.2 Load Modulation Behavior of Doherty Amplifier With Optimized Carrier Amplifier

To properly design a Doherty amplifier using a real device, the knee voltage effect should be considered as described in Section 2.2.1. Fig. 2.14 shows the operational diagram of the Doherty amplifier used to analyze the load modulation behavior. Compared with the conventional one, it has a scaled load impedance of Z_L/δ. δ represents the increased resistance ratio to achieve the fully saturated operation of the carrier amplifier at the 6 dB back-off region. For the analysis, it is assumed that each current source is linearly proportional to the input voltage with the maximum current of I_max. The ideal harmonic short circuits are provided so that the output power and efficiency can be determined by only the fundamental and dc components.

The load impedances of the carrier and peaking amplifiers are determined by their current ratio through the load modulation. The peaking amplifiers for the both cases of the with/without knee effect can generate the proper output current. However, since the load impedance at the 6 dB back-off power region of the carrier amplifier with the knee effect is larger than that of the amplifier without the knee effect, the current of the carrier amplifier cannot reach to the maximum value by the load modulation, leading to the degradation of output power. For the proper current generation, the peaking amplifier should generate more current at the peak power, by γ times, than the carrier amplifier.

The fundamental currents, as a function of the input voltage, of the conventional Doherty amplifier and the Doherty amplifier with the knee effect, are represented in Fig. 2.15, The currents, I_C, I_P, I_DC,C and I_DC,P which represent the fundamental and dc currents of the carrier and peaking amplifiers with the knee effect, respectively, are derived as

$\begin{array}{cc}{I}_C=\frac{I_{1,C}\left({\theta }_c\right)}{V_{\mathrm{in},\text{max}}}\bullet v_{\mathrm{in}},& 0\le v_{\mathrm{in}}\le \frac{\gamma \beta +1}{2\gamma }\bullet V_{\mathrm{in},\text{max}}\end{array}$

$\begin{array}{cc}{I}_{DC,C}=\frac{I_{\mathit{dc},C}\left({\theta }_c\right)}{V_{\mathrm{in},\text{max}}}\bullet v_{\mathrm{in}},& 0\le v_{\mathrm{in}}\le \frac{\gamma \beta +1}{2\gamma }\bullet V_{\mathrm{in},\text{max}}\end{array}$

$I_P=\left\{\begin{array}{cc}0,& 0\le v_{\text{in}}\le \left(\beta /2\right)V_{\text{in},\text{max}}\\ \gamma \bullet \sigma \bullet I_{1,p}\left({\theta }_p\right)\bullet \left(\frac{v_{\text{in}}}{V_{\text{in},\text{max}}}-\frac{\beta }{2}\right),& \left(\frac{\beta }{2}\right)V_{\text{in},\text{max}}\le v_{\mathit{in}}\le \left(\mathit{\gamma \beta }+1\right)V_{\text{in},\text{max}}/2\gamma \end{array}\right.$

$I_{\mathit{DC},P}=\left\{\begin{array}{cc}0,& 0\le v_{\text{in}}\le \beta \bullet V_{\text{in},\text{max}}/2\\ \gamma \bullet \sigma \bullet I_{\mathit{dc},p}\left({\theta }_p\right)\bullet \left(\frac{v_{\text{in}}}{V_{\text{in},\text{max}}}-\frac{\beta }{2}\right),& \left(\frac{\beta }{2}\right)V_{\text{in},\text{max}}\le v_{\text{in}}\le \left(\mathit{\gamma \beta }+1\right)V_{\text{in},\text{max}}/2\gamma \end{array}\right.$

Here, I_1,C and I_dc,_C are the fundamental and dc currents of the carrier amplifier with the conduction angle of θ_c, which are defined in (2.21) and (2.22).

$I_{1,p}\left({\theta }_p\right)=\frac{I_{\max }}{2\pi }\bullet \frac{{\theta }_p-sin{\theta }_p}{1-cos\left({\theta }_p/2\right)}$

$I_{\mathit{dc},p}\left({\theta }_p\right)=\frac{I_{\max }}{2\pi }\bullet \frac{2\bullet sin\left({\theta }_p/2\right)-{\theta }_p\bullet cos\left({\theta }_p/2\right)}{1-cos\left({\theta }_p/2\right)}$

$\beta =\frac{2\bullet i_{\max }^{″}}{I_{\max }}=\frac{V_{\mathit{dc}}-\sqrt{{\left(V_{\mathit{dc}}\right)}^2-2\bullet V_k\bullet \left(V_{\mathit{dc}}-V_k\right)}}{V_k}$

$\sigma =\frac{2\bullet I_{1,c}\left({\theta }_c\right)}{I_{1,p}\left({\theta }_p\right)}$

As explained in Section 2.2.1, the carrier amplifier with the knee effect has a load impedance at the 6 dB back-off power point which is larger than 2R_OPT, and the voltage swing of the amplifier is increased, as shown in Fig. 2.11B. To generate the first peak efficiency at the 6 dB back-off level, the current of the knee effect Doherty amplifier should be lower than that of the conventional Doherty amplifier by β as described previously. Due to the lower current, the input power at the 6 dB back-off is lower, and the input power for the peak power generation is also reduced as shown in Fig. 2.15. To get the proper modulation, the peaking amplifier should be overdriven by a factor of γ, which will be derived later. σ indicates the uneven power input drive ratio between the carrier and peaking amplifiers.

Using the currents of the carrier and peaking amplifiers, the load impedances of the two amplifiers can be calculated:

$Z_C=\left\{\begin{array}{cc}\frac{\delta \bullet Z_T^2}{Z_L},& 0\le v_{\text{in}}\le \frac{\beta }{2}\bullet V_{\text{in},\max }\\ \frac{\delta \bullet Z_T^2}{Z_L\bullet \left[1+\frac{I_P}{I_C^{\prime }}\right]},& \frac{\beta }{2}\bullet V_{\text{in},\max }\le v_{\text{in}}\le \frac{\mathit{\gamma \beta }+1}{2\gamma }{V}_{\text{in},\max }\end{array}\right.$

$Z_P=\left\{\begin{array}{cc}\infty ,& 0\le v_{\text{in}}\le \frac{\beta }{2}\bullet V_{\text{in},\text{max}}\\ \frac{Z_L}{\delta }\bullet \left(1+\frac{I_C^{\prime }}{I_P}\right),& \frac{\beta }{2}\bullet V_{\text{in},\text{max}}\le v_{\text{in}}\le \frac{\mathit{\gamma \beta }+1}{2\gamma }{V}_{\text{in},\text{max}}\end{array}\right.$

where

$\delta =\frac{R^{\text{Case}\_\mathrm{II}}}{R^{\text{Case}\_\mathrm{I}}}=\frac{V_{\mathit{dc}}+\sqrt{{\left(V_{\mathit{dc}}\right)}^2-2\bullet V_k\bullet \left(V_{\mathit{dc}}-V_k\right)}}{2\bullet \beta \bullet \left(V_{\mathit{dc}}-V_k\right)}$

Using the lossless quarter-wave transmission line in Fig. 2.14, I′_C is calculated:

$I_C^{\prime }=\delta \bullet I_C\bullet \frac{Z_T}{Z_L}-I_P$

Since the carrier amplifier of the knee effect Doherty amplifier has a larger load impedance than the conventional Doherty, the carrier amplifier operates in the heavily saturated region after the peaking amplifier is turned on. To prevent the saturated operation of the carrier amplifier, the load impedance of the carrier amplifier should be lowered by generating more current from the peaking amplifier. Thus, the peaking amplifier should be overdriven by a factor of γ. For linear operation of the carrier amplifier without voltage clipping, the voltage across the current source of the carrier amplifier should satisfy the following condition at the maximum input voltage:

$Z_C\bullet I_C\le V_{\mathit{dc}}-\frac{\mathit{\gamma \beta }+1}{2\gamma }\bullet V_k$

From Eq. (2.44), γ can be inferred:

$\gamma \ge \frac{2\delta R_{\mathrm{OPT}}{I}_{1,C}\left({\theta }_c\right)+V_k}{2V_{\mathit{dc}}-2R_{\mathrm{OPT}}{I}_{1,C}\left({\theta }_c\right)\left(\mathit{\beta \delta }-1\right)-\beta V_k}$

In this analysis, it is assumed that Z_T = R_OPT and Z_L = R_OPT/2. δ represents the R^Case_I to R^Case_II ratio to achieve the fully saturated operation of the carrier amplifier at the back-off region. For the conventional case, δ, γ, and β are equal to 1. Thus, the fundamental load impedance of the carrier amplifier is modulated from 2R_OPT to R_OPT, while that of the peaking amplifier varies from ∞ to R_OPT. On the other hand, for the knee effect Doherty amplifier, δ and γ are > 1, but β is < 1. Thus, the fundamental load impedances of the carrier and peaking amplifiers are modulated from 2δR_OPT to 2R_OPT {δ(γβ + 1)− γ}/(γβ + 1) and from ∞ to R_OPT (γβ + 1)/2γ, respectively, as described in Fig. 2.16A. To explore the load modulation behavior, V_k of 4 V is assumed, and R_OPT is calculated using Eq. (2.20). At the low-power region (0 ≤ v_in ≤ βV_in,max/2), the load impedance of the carrier amplifier is larger than 2R_OPT, that is, 2δR_OPT. At the high-power region (βV_in,max/2 ≤ v_in ≤ (γβ + 1)V_in,max/2γ), the load impedance maintains a value larger than conventional amplifier. In contrast, the load impedance of the peaking amplifier sustains a smaller value than that of the conventional amplifier; this results in a slight power degradation.

Fig. 2.16B shows the resulting fundamental voltages of the carrier and peaking amplifiers for the conventional and knee effect Doherty amplifiers. As expected, the carrier amplifier with the knee effect has a larger fundamental voltage at the 6 dB back-off because of the larger load impedance. Therefore, the carrier amplifier can be fully saturated, delivering the high efficiency.

Using the currents and load impedances of the carrier and peaking amplifiers, the efficiency is estimated through MATLAB. Fig. 2.17 represents the calculated efficiencies based on the above analysis for the θ_c = 210° and θ_p = 150° operation. To calculate the efficiencies, δ, β, σ, and γ are determined based on V_dc, V_k, I_1,c(θ_c), and I_1,p(θ_p), which are 30 V, 4 V, 4.2129 A, and 3.6384 A, respectively. The resulting δ, β, σ, and γ are 1.1725, 0.9235, 2.3158, and 1.2494, respectively. In the low-power region, the knee effect Doherty amplifier has higher efficiency than that of the conventional amplifier because of the larger load impedance. In particular, the knee effect Doherty amplifier delivers its maximum efficiency of 67.9% at the 6 dB back-off output power, which is an increase of about 5% compared with the conventional one. Although the maximum output power and efficiency at the maximum output power are slightly degraded because of the imperfect load modulation, the knee effect Doherty scheme improves efficiency for amplification of a modulated signal without any additional circuitry. Since the currents and voltages of the carrier and peaking amplifiers are different, the impedances are mismatched at the peak power. This mismatch problem can be solved by the offset line control, which will be described in Section 2.3.

2.3.1 Phase Variation of the Peaking Amplifier

To analyze the load modulation behavior of the Doherty amplifier, the amplifier model is simplified as shown in Fig. 2.18. The carrier and peaking currents are normalized to the peak current and have variable phases. Because the offset line compensates the output capacitance effects of the device, the amplifier with the offset line can be substituted by an ideal current source with an impedance level of R_o.

Fig. 2.19A shows the simulated results of the load modulations for the carrier and peaking amplifiers, without the additional offset line, as the output power of the amplifier is increased. Without the phase variation of the peaking amplifier, the output loads of the carrier and peaking amplifiers are ideally modulated from 100 to 50 Ω and infinite to 50 Ω, respectively, following the resistive load. However, the peaking amplifier has a negative phase variation as shown in Fig. 2.19B, which is extracted from Cree CGH40045 GaN device model. With the phase variation, the output loads of the carrier and peaking amplifiers are properly matched at the two maximum efficiency points, and the load cannot be properly modulated between the two points as shown in Fig. 2.19A. The improper load modulation degrades the efficiency of the Doherty amplifier.

This load mismatch problem can be solved somewhat by inserting additional offset lines at the carrier and peaking amplifiers. In addition, the new offset lines increase the load impedances of the carrier and peaking amplifiers, mitigating the knee effect of the carrier amplifier as described in Section 2.2 and enhancing the efficiency of the Doherty amplifier.

2.3.2 Load Modulation of Peaking Amplifier With the Additional Offset Lines

To solve the phase variation problem of the peaking amplifier, additional offset lines having delays of θ_ac and θ_ap are added at the outputs of the current sources as shown in Fig. 2.18. In this Doherty amplifier, the relationship between the normalized carrier current I_c and normalized peaking current I_p are given by

$I_c=\frac{1+I_p}{2}{e}^{j\left(\frac{1}{4}\pi +{\theta }_{\mathit{ac}}+{\theta }_{\mathit{ap}}\right)}$

With only the additional peaking offset line (θ_ac = 0), the impedances Z_p and Z_c, defined in Fig. 2.18, are expressed in terms of I_p as

$Z_p=\frac{Z_0^2}{2R_L}\left(\left(1+\frac{1}{I_p}\right)+jtan{\theta }_{\mathit{ap}}\left(1-\frac{1}{I_p}\right)\right)$

$Z_c=Z_0\left(\frac{Z_0}{R_L}-\frac{2I_p}{1+I_p}+jtan{\theta }_{\mathit{ap}}\left(1-\frac{2I_p}{1+I_p}\right)\right)$

Fig. 2.20 shows the load modulation curves calculated by Eq. (2.47) for the case with the additional offset line but without the peaking amplifier phase variation. The phase variation of the modulated loads with a negative length of the additional offset line is opposite to the phase variation due to the peaking amplifier phase variation shown in Fig. 2.19, indicating that the phase variation of the peaking amplifier can be compensated by shorting the conventional offset line, but at the expense of the carrier matching. We will also address the carrier amplifier problem in the next section.

If there is a phase difference between the carrier and peaking amplifiers (θ_d), Z_p in Eq. (2.47) is expressed by

$Z_p=\frac{1+I_p}{2I_p}\left(cos{\theta }_d-tan{\theta }_{\mathit{ap}}sin{\theta }_d\right)+j{Z}_0\left(tan{\theta }_{\mathit{ap}}-\frac{1+I_p}{2I_p}\left(sin{\theta }_d+cos{\theta }_{d}tan{\theta }_{\mathit{ap}}\right)\right)$

To minimize the imaginary term of the Z_p, θ_ap should be

${\theta }_{\mathit{ap}}={tan}^{-1}\left(\frac{\frac{1+I_p}{2I_p}sin{\theta }_d}{1-\frac{1+I_p}{2I_p}cos{\theta }_d}\right)$

Because the phase of the peaking amplifier linearly decreases from 0 to θ_d,max with the I_p as shown in Fig. 2.19B, Eq. (2.49) can be rearranged to

${\theta }_{\mathit{ap}}={tan}^{-1}\left(\frac{\frac{1+I_p}{2I_p}sin\left\{\left(I_p-1\right){\theta }_{d,\text{max}}\right\}}{1-\frac{1+I_p}{2I_p}cos\left\{\left(I_p-1\right){\theta }_{d,\text{max}}\right\}}\right)$

The calculated additional offset line lengths with the linear phase variation of the peaking amplifier with θ_d,max of − 60 to − 45° are shown in Fig. 2.21. Although the required additional offset line length is different according to the I_p, the difference is not much. Therefore, it is possible to compensate the phase variation of the peaking amplifier by adjusting the length of the offset line.

With the calculated additional offset line length required at the I_p of 0.5, the load modulation prolifes of the carrier and peaking amplifier are shown in Fig. 2.22. As analyzed by Eq. (2.50), the load modulation of the peaking amplifier with the additional peaking offset line is near to the ideal Doherty load modulation.

However, due to the additional peaking offset line with the negative length, the impedance toward the peaking amplifier (at Z_p′ in Fig. 2.18) is not an open but an inductive impedance. This impedance affects the load modulation of the carrier amplifier as shown in Fig. 2.22.

2.3.3 The Load Modulation of the Carrier Amplifier With the Additional Offset Lines

For the proper load modulation of the carrier amplifier with the additional peaking offset line, the phase angle of Z_c when the peaking amplifier is in the off- state should be minimized. To convert the carrier load to a resistive load, an additional offset line is needed at the output of the carrier amplifier also. Fig. 2.23 shows the load modulation of the Doherty amplifier according to the additional carrier offset line but without the phase variation of the peaking amplifier. With the negative length of additional offset line (shorten the conventional offset line), Z_c at the low-power region becomes an inductive impedance, which can absorb the impedance variation generated by the compensation of the peaking amplifier phase variation. With the negative additional carrier offset line, the load modulation of the peaking amplifier becomes slightly inductive. Therefore, if the negative additional offset line is added at the carrier amplifier, the additional peaking offset line should be a little lengthened.

Fig. 2.24A shows the load modulation of the Doherty amplifier with the additional offset lines. To compensate the phase variation of the peaking amplifier (Fig. 2.19B), the additional offset lines for the carrier and peaking amplifiers are set to − 43° and − 13°, respectively. The load of the peaking amplifier is modulated similarly to the ideal case. The load of the carrier amplifier does not closely follow the ideal modulation, but the phase variation is small, and the impedance deviation is also small. The magnitude of Z_c at the low-power region is larger than that with the conventional offset line.

With the larger load for the carrier amplifier, the efficiency at the low-power region is increased. Moreover, the load modulation is ideal for the Doherty amplifier with the knee voltage effect as discussed in Section 2.2. As discussed before, the load of the carrier amplifier could not be properly matched at 50 Ω due to the larger load modulation range required for the carrier amplifier. However, with these offset lines, both the larger load of the carrier amplifier at the low power region and the proper power match at the peak output power can be realized simultaneously as shown in Fig. 2.24B.

In addition, the Z_p is resistive with the larger value than the ideal Doherty modulation. Due to the larger load of the peaking amplifier during the load modulation, the peaking amplifier can get a high efficiency, even higher than that of the ideal Doherty amplifier. In Fig. 2.24B, Z_c of the Doherty amplifier with the additional offset lines starts to modulate from the − 5 dB output power back-off level, not − 6 dB, because the output power delivered from the ideal current source is proportional to the magnitude of the load. However, the output power delivered from a real transistor is decreased for the larger load, and the Z_c is modulated at the output power back-off level larger than  5dB as shown in the following section.

2.3.4 Simulation Results With Real Device

To validate the investigations in the previous sections, we have designed a symmetrical Doherty amplifier (Fig. 2.25). The Doherty amplifier is designed at the 1.94 GHz using GaN pHEMT devices (Cree CGH40045) with the drain bias of 50 V. The gate of the peaking amplifier is biased at − 6 V, and the phase of the amplifier is varied from 0° to − 50°. For the conventional offset line design, the offset line lengths of the carrier and peaking amplifiers are 50°. For the new offset line design, the offset line lengths of the carrier and peaking amplifiers should be 37° (− 13° of θ_ac) and 10° (− 40° of θ_ap), respectively. For comparison, the Doherty amplifier without the phase variation of the peaking amplifier is also designed. This amplifier is identical to the adaptive phase control to compensate the phase variation of the peaking amplifier using the dual input Doherty structure.

Figs. 2.26 and 2.27 show the load modulation behaviors of the carrier and peaking amplifiers under the three different operation conditions. When the conventional offset lines are added, the phase variation of the peaking amplifier disturbs the load modulation. The improper modulation can be compensated either by the additional offset lines or by the adaptive phase control at the dual input structure (equivalent to the without peaking phase variation and conventional offset lines). The load modulation is examined for the reference planes defined by Z_c1 and Z_p1 shown in Fig. 2.25 for the three cases with/without the peaking amplifier phase variation and the new offset line with the phase variation. Following the expectation explained at Section 2.3.3, Z_p1 with the new offset is modulated following the resistive load with a larger magnitude. Z_c1 with the new offset line still has an imaginary component during the load modulation, but the magnitude of the Z_c1 at the low-power region is larger than that with the conventional offset line. The load modulation is started at −6 dB back-off power level.

Fig. 2.28 shows the efficiencies of the carrier and peaking amplifiers. Due to the larger Z_c1 with the new offset line, the efficiency of the carrier amplifier is higher at the low-power region than those of the other operation conditions. However, the imaginary component of the load still exists, and the efficiency of the carrier amplifier at the high-power region is a little lower than that without the phase variation and similar to that with the conventional offset line. The efficiency of the peaking amplifier with the new offset line is higher than those with the other cases at the all output power region since the magnitude of the Z_p1 is larger than those of the other cases.

Fig. 2.29 shows the simulated CW performance of the Doherty amplifier. With the new offset line, the efficiency of the Doherty amplifier is higher at the low-power region. At the high-power region, the efficiency of the carrier amplifier is lower than that without the phase variation. However, the efficiency of the peaking amplifier is higher, and the efficiency of the Doherty amplifier at the high-power region is similar to that without the phase variation. Therefore, the Doherty amplifier with the new offset line not only provides a higher efficiency than that with the conventional offset line but also has a higher efficiency than that without the phase variation of the peaking amplifier. Gain characteristic does not show much difference for the three cases. However, due to the larger load operation of the carrier amplifier, the gain of the Doherty amplifier with the new offset line shows early compression characteristic.