IEEE Circuits and Systems Magazine - Q4 2020 - 57

b inj_c 2 b inj_p (31)

To satisfy this, the deep Class-AB and deep Class C
are selected for the carrier and peaking device, respectively.
Furthermore, the mathematical expression of b d in
[38] can be calculated to be

bd = c 1 +

a inj_p
b inj_p
mc 1 +
m^1 + a h (32)
v 1c + v 2c
i 1c - i 2c

With the values of the first and second brackets of (32)
always being larger than 1 due to the presence of ainj_p
and b inj_p, b d is also increased due to an increase in a .
Since the Doherty PA has a modulation of Zcarrier
(from 2 Ropt to Ropt) and Zpeaking (from infinity impedance
to Ropt), a phase variation of Vload c/p and thus the AM-PM
distortion of the proposed Doherty PA is unavoidable.
For the carrier and peaking PA, the absolute values of
gm1 in the proposed Doherty PA is smaller than for a conventional Doherty PA (shown in Fig. 13). This results in a
smaller CgdâÂ·âgm1, which improves the AM-PM distortion.
Their output voltage phase can be rewritten [36, 58] as,
R S + rg
p,
1
~ ^ C gs - ^C gd g m1 h . Z carrier h
Z carrier ! ^2R opt, R opth
(33)

TPhase ^VLoad_c h .= tan -1

fX S

R S + rg
TPhase ^VLoad_p h .= tan -1
fX p,
1
S
~ ^ C gs + ^ C gd g m1 h . Z peaking h
Z peaking ! ^3, R opth

(34)

when viewed on the Smith chart have a smaller variation at saturation thus load modulation can be achieved
over a wider frequency range. The fabricated Doherty
PA in [36] is shown in Fig. 14.
In [39], a compact output combiner for broadband
Doherty PA was introduced. In order to compensate for
the bandwidth limiting effect that occurs in the conventional microstrip combiner, a grounded quarter wavelength was added to the output of the peaking amplifier.
Frequency response analysis also verified that the carrier impedance can be maintained steadily across a large
frequency range with the help of such kind of topology,
resulting in enhanced bandwidths.
Advantage of the non-infinite output impedances of
the peaking amplifier was taken advantage of for the
broadband continuous-mode Doherty PA [50]. In particular, the carrier PA load impedance variation versus
the load impedance of the peaking PA was derived. With
the help of this, the carrier PA operated in a continuous
class-J mode before the OBO point, where the load impedance of the peaking PA had some influences on the
harmonic terminations of the carrier PA.

0.02
Transfer Function

To obtain the waveform shown in Fig. 12, a higher 2f0
injected current from the carrier device than one from
the peaking device is a required.

B AB

Peaking
0.01 Device

A
gm3
gm1

Carrier
Device

0
Peaking
-0.01 Device

Conventional DPA
Proposed DPA

-0.02
Carrier Device

vGS,bias

Figure 13. Transconductance gmn versus different gate bias.

When the HIN is inserted between the carrier and peaking FII, over a wide frequency range, the " open-circuited "
characteristic of HIN at the fundamental frequency cannot
always be maintained. This reduces the Doherty PA bandwidth. A coupled PCN was proposed to eliminate the reduction in bandwidth. Zoe, Zoo are the even and odd mode
impedances of the coupled section, respectively, and i
represents its electrical length. The ratio between Zoe and
Zoo is defined by t . Coupling C, and t are related by

C = - 20 log

t-1
= - 20 log c 1 - 2 m (35)
t+1
t+1

A smaller external Q factor (QE) for the entire peaking
branch can be obtained when the PCN has a strong coupling. Consequently, the frequency behaviors of Zpeaking
FOURTH QUARTER 2020

Figure 14. Photograph of the fabricated Doherty PA in [36].

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IEEE Circuits and Systems Magazine - Q4 2020

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