IEEE Circuits and Systems Magazine - Q4 2020 - 56

The related voltage waveforms are shown in Fig. 11.
The purpose of second harmonic injection is to enhance
the amplitude of the fundamental voltage swing with respect to a non-injected design.

Voltage Amplitude

2

	

1.5
0.5
0
-0.5
0

0.5

1
Time (ms)

1.5

2

vD (Ït ) = v1cos (Ït )
vD (Ït ) = v1cos (Ït ) + (v2 + ainj_c/p)cos(2 Ït )
vD (Ït ) = v1cos (Ït ) + v2cos (2Ït )
Figure 11. Voltage waveform of active device under 180Â°
harmonic injection and non-harmonic injection in [36].

2
1.5
1
0.5

RCT > 1
(Carrier
Device)

0
-0.5
-1
-1.5

RCT = I self c/p ^2f0 h /I inj p/c ^2f0 h (26)

Where Iself c/p (2f0) is the device self-generated 2f0 component and Iinj p/c (2f0) is the injected 2f0 component from
the other device.

1

-1

Current Amplitude

For the current waveforms, their shapes are also
modulated by the injected 2f0 components with two conditions, which is shown in Fig. 12. A parameter, named
relative current ratio (RCT), is defined to demonstrate
these two conditions.

0

0.5

RCT < 1
(Peaking
Device)

1
Time (ms)

Flatten
Top

1.5

2

iD (Ït ) = i1cos (Ït )
iD (Ït ) = i1cos (Ït ) - i2cos (2Ït )
&

i1cos (Ït ) - i2cos (2Ït ) + bini_c/p cos(2Ït )
(RCT > 1 and RCT <1)

Figure 12. Current waveform of the active device under 180Â°
harmonic injection and non-harmonic injection in [36].

	

I DD = 0, i 1 = 1, i 2 = 0.3 and b inj c/p = 0.2 RCT 2 1(27)

	

I DD = 0, i 1 = 1, i 2 = 0.2 and b inj c/p = 0.3 RCT 1 1(28)

For the condition of RCT21, the current bifurcation
caused by the active device self-generated 2f0 can be
mitigated, but the amplitude increase is minimal. For the
condition where RCT11, the flattened waveform is fully
mitigated and the amplitude is increased.
RCT11 was then chosen for the peaking device to
realize enough power. Meanwhile, Iinj p (2f0) is inevitably
smaller than Iself c (2f0), which results in RCT21 being
used for the carrier device. Psat,p, Psat,c, and its corresponding a of the Doherty PA with and without 180Â° HIN
is shown in Table I.
As shown in the table, the a can only be solved when
the following condition is satisfied
^V1p + V2p + a inj_c h^ i 1p - i 2p + b inj_c h
^ V1p + V2p h^ i 1p - i 2p h
2
^ V1c + V2c + a inj_p h^ i 1c - i 2c + b inj_p h
^ V1c + V2ch^ i 1c - i 2ch

(29)
In (29), both ainj-c and ainj-p are relatively small compared
to (V1p + V2p) and (V1c + V2c) . Hence, the influence of ainj-c
and ainj-p on the voltage amplitude ratio is negligible.
	

^V1p + V2p + a inj_c h
^ V 1p + V 2p h
.
(30)
^V1c + V2c + a inj_p h
^ V 1c + V 2c h

Table I.
Psat,p, Psat,c, corresponding a of Doherty PA with and without 180Â° HIN in [36].
Doherty PA With 180Â° HIN

Doherty PA Without 180Â° HIN

Psat,c

0.5*
^ V1c + V2c + a inj_p h^ i 1c - i 2c + b inj_p h

0.5*
^ V1c + V2c h^ i 1c - i 2c h

Psat,p

0.5*
^ V1p + V2p + a inj_c h^i 1p - i 2p + b inj_c h

0.5*
^ V1p + V2p h^i 1p - i 2p h

a

56â	

^V1p + V2p + a inj_c h^i 1p - i 2p + b inj_c h
^ V1c + V2c + a inj_p h^ i 1c - i 2c + b inj_p h

IEEE CIRCUITS AND SYSTEMS MAGAZINE 		

^ V1p + V2p h^i 1p - i 2p h
^ V1c + V2c h^i 1c - i 2c h
FOURTH QUARTER 2020
IEEE Circuits and Systems Magazine - Q4 2020

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