RF Power Amplifier Tutorial (1)

Tomomi Research Inc.
RF Power Amplifier Tutorial (1)
2016/07/20
Seong-Hun Choe

Gain
Power
Amplifier
(PA)
Gain (G)Pin Pout
𝐺 𝑑𝐵 = 10 𝑙𝑜𝑔10 電力比 = 10 𝑙𝑜𝑔10
𝑃𝑜𝑢𝑡
𝑃𝑖𝑛
10 dB
-3dB

Gain written as a voltage
𝐺 𝑑𝐵 = 10 log 電力比 = 10𝑙𝑜𝑔10
𝑃𝑜𝑢𝑡
𝑃𝑖𝑛
= 10 𝑙𝑜𝑔10
𝑉𝑜𝑢𝑡
2
𝑅 𝑜𝑢𝑡
𝑉𝑖𝑛
2
𝑅𝑖𝑛
Let R1 = R2
𝐺 𝑑𝐵 = 10𝑙𝑜𝑔10
𝑉𝑜𝑢𝑡
2
𝑅 𝑜𝑢𝑡
𝑉𝑖𝑛
2
𝑅𝑖𝑛
= 10𝑙𝑜𝑔10
𝑉𝑜𝑢𝑡
2
𝑉𝑖𝑛
2
= 20𝑙𝑜𝑔10
𝑉𝑜𝑢𝑡
𝑉𝑖𝑛

Gain written as a Current
𝐺 𝑑𝐵 = 10 log 電力比 = 10 𝑙𝑜𝑔10
𝑃𝑜𝑢𝑡
𝑃𝑖𝑛
= 10𝑙𝑜𝑔10
𝑅 𝑜𝑢𝑡 𝐼 𝑜𝑢𝑡
2
𝑅𝑖𝑛 𝐼𝑖𝑛
2
Let R1 = R2
𝐺 𝑑𝐵 = 10𝑙𝑜𝑔10
𝑅 𝑜𝑢𝑡 𝐼 𝑜𝑢𝑡
2
𝑅𝑖𝑛 𝐼𝑖𝑛
2 = 10𝑙𝑜𝑔10
𝐼 𝑜𝑢𝑡
2
𝐼𝑖𝑛
2 =
= 20 𝑙𝑜𝑔10
𝐼 𝑜𝑢𝑡
𝐼𝑖𝑛

Gain Summary
Expression
Power [dB]
10 𝑙𝑜𝑔10
𝑃𝑜𝑢𝑡
𝑃𝑖𝑛
Voltage [dB]
20 𝑙𝑜𝑔10
𝑉𝑜𝑢𝑡
𝑉𝑖𝑛
Current [dB]
20 𝑙𝑜𝑔10
𝐼 𝑜𝑢𝑡
𝐼𝑖𝑛

Transitor Data Sheet
2sC3356 (Renesas Electronics)
http://jp.rs-online.com/web/p/bipolar-transistors/7724980/
𝑆11 = 0.26
トランジスタの入力側（Base)にインピーダンス
整合回路を設けずに、50Ohmの信号発生器
から1GHzの信号を入力すると、(0.26)^2*100
= 6.8%の電力の反射が起こることを意味
http://amplet.tokyo/tu/pdf/2sc3356.pdf

𝑆22 = 0.266
トランジスタの出力側（Collector)にインピーダ
ンス整合回路を設けずに、50Ohmの信号発
生器から1GHzの信号を入力すると、
(0.266)^2*100 = 7.1%の電力の反射が起こる
ことを意味

𝑆21 = 3.744
トランジスタに電源を供給し、インピーダンス
整合回路を設けずに、50Ohmの信号を入力
すると、10log(3.744)^2=11.5 dBの利得（ゲイ
ン）があることを意味する。

𝑆12 = 0.136
トランジスタの出力側（Collector)にインピーダ
ンス整合回路を設けずに50Ohm系の信号発
生器から1GHzの信号を入力すると、
10Log(0.236)^2=-17.3dBが減衰してトランジス
タの入力側(Base)に出力されることを意味す
る。

dB(デシベル）：
物理量のレベルを表す単位。無次元量である。
dBm :
電力を表す単位である。要はWattに変換ができる単位。dBと混同しないように注意。
0 [dBm] = 1 [mW]
𝑑𝐵𝑚 = 10𝑙𝑜𝑔10(𝑚𝑊)
dBmとdB
Power [mW] Power [dBm]
1 mW 0dBm=10 𝑙𝑜𝑔10(1)
10 mW 10dBm=10 𝑙𝑜𝑔10(10)
100 mW 20dBm=10 𝑙𝑜𝑔10(100)
1W 30dBm=10 𝑙𝑜𝑔10(1000)
10W 40dBm=10 𝑙𝑜𝑔10(10000)

dBmとGain
Power
Amplifier
(PA)
Gain (G)
= 25 [dB]
Pin= 1 mW Pout= ?
Pout[dBm] = Pin [dBm] + Gain [dB]
= 0 [dBm] + 25 [dB]
= 25 [dBm]
= 10 ^ (25/10) = 316.22 [mW]𝑑𝐵𝑚 = 10𝑙𝑜𝑔10 𝑚𝑊
𝑚𝑊 = 10
𝑑𝐵𝑚
10

dBmとGain
Power [mW] Power [dBm]
1 mW 0dBm=10𝑙𝑜𝑔10(1)
10 mW 10dBm=10𝑙𝑜𝑔10(10)
100 mW 20dBm=10𝑙𝑜𝑔10(100)
1W 30dBm=10𝑙𝑜𝑔10(1000)
10W 40dBm=10𝑙𝑜𝑔10(10000)
http://www.ebay.com/itm/182194447106?_trksid=p2057872.
m2749.l2649&ssPageName=STRK%3AMEBIDX%3AIT

この表でゲインを計算（次のページ）
http://www.ebay.com/itm/141841663164?_trksid=p2057872.
m2749.l2649&ssPageName=STRK%3AMEBIDX%3AIT

14 MHz
input power
[W]
input power
[Vpp]
output power
[W]
output power
[Vpp]
Gain at 14 MHz
[Power]
Gain at 14 MHz[Voltage
]
0.5 14.2 9.7 60.4 12.88 12.57
1 20 18.5 83.2 12.67 12.38
2 28 33 110 12.17 11.88
3 35 46 128 11.86 11.26
4 40 54 141 11.30 10.94
5 45 60 148 10.79 10.34
5.3 46 64 151 10.82 10.32
7 MHz
input power
[W]
input power
[Vpp]
output power
[W]
output power
[Vpp]
Gain at 7MHz [Power]
Gain at 7 MHz [Voltage
]
0.1 6.3 1.66 26.6 12.20 12.51
0.5 14 27 104 17.32 17.42
1 20 55 146 17.40 17.27
2 28 93 196 16.67 16.90
3 35 106 208 15.48 15.48
4 40 112 213 14.47 14.53
5 45 114 214 13.58 13.54

12.20
17.3217.40
16.67
15.48
14.47
13.58
12.8812.67 12.17 11.86 11.30 10.7910.82
0
2
4
6
8
10
12
14
16
18
20
0 2 4 6
Gain[dB]
input power [W]
Gain at 7MHz [Power]
Gain at 14 MHz [Power]
1.66
27
55
93
106
112 114
9.7
18.5
33
46
54
60
64
0
20
40
60
80
100
120
0 2 4 6
Outputpower[W]
input power [W]
output power at 7MHz [W]
output power at 14 MHz
[W]
Input power vs. Output power
これがまっすぐだとLinear Ampと呼ばれる
Input powerによるGainの変化。まあまあまっすぐ

Efficiency definitions in RF Power Amplifier
Matching
Network
Matching
Network
Load
Driver
Pin
Pout
Pdc
+Vdc
L
Gain : Gp

Collector Efficiency
𝜂 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟 =
𝑃𝑜𝑢𝑡
𝑃𝑑𝑐
Bipolar transistors (BJTs)
Po : the RF output power
Pdc: the input power supplied by the DC supply to the collector
(Pdc = Vdc*Idc)
Gain : Gp

OVERALL Efficiency
𝜂 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 =
𝑃𝑜𝑢𝑡
𝑃𝑖𝑛 + 𝑃𝑑𝑐
𝑃𝑜𝑢𝑡 = 𝐺 𝑝 𝑃𝑖𝑛
𝑃𝑜𝑢𝑡
𝑃𝑜𝑢𝑡
𝐺 𝑝
+ 𝑃𝑑𝑐
Gain, P_out, P_dcだけで、効率を表す。
Gain : Gp

POWER ADDED efficiency
𝜂 𝑃𝑜𝑤𝑒𝑟 𝑎𝑑𝑑𝑒𝑑 =
𝑃𝑜𝑢𝑡 − 𝑃𝑖𝑛
𝑃𝑑𝑐
𝑃𝑜𝑢𝑡 = 𝐺 𝑝 𝑃𝑖𝑛
Gain, P_out, P_dcだけで、効率を表す。
𝑃𝑜𝑢𝑡 −
𝑃𝑜𝑢𝑡
𝐺 𝑝
𝑃𝑑𝑐
Gain : Gp

Example
100W
150W
Gain , Gp = 10
equation Value
Collector efficiency
𝜂 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟 =
𝑃𝑜𝑢𝑡
𝑃𝑑𝑐
66.7% = 100/150
Overall efficiency
𝑃𝑜𝑢𝑡
𝑃𝑜𝑢𝑡
𝐺 𝑝
+ 𝑃𝑑𝑐
62.5%=100/(100/10+150)
Power added efficiency
𝑃𝑜𝑢𝑡 −
𝑃𝑜𝑢𝑡
𝐺 𝑝
𝑃𝑑𝑐
60%=(100-100/10)/150

Power output Capability
Matching
Network
Load
Pout
Pdc
+Vdc
L
Gain : Gp Vc,pk
Ic,pk
Collectorからいくら電力が取り出せるかを表すパラメータ
The output power produced when the device has a peak
collector voltage of 1[V] and a peak collector current of 1 [A].
𝐶 𝑃 =
𝑃𝑜𝑢𝑡
𝑁 𝐼 𝐶,𝑝𝑘 𝑉𝑐,𝑝𝑘
Cp : power output capability
Pout : output power [W]
N : number of transistors in parallel or
push pull design
Ic,pk : the peak collector current[A]
Vc,pk : the peak collector voltage [V]
Important for cost effective design

Example
A single ended class E circuit :
Theoretical power output capability Cp, class E = 0.0981
The designed the peak collector voltage Vc,pk = 100 [V]
The peak current will be
𝐶 𝑃 =
𝑃𝑜𝑢𝑡
𝑁 𝐼 𝐶,𝑝𝑘 𝑉𝑐,𝑝𝑘
𝐼 𝐶,𝑝𝑘 =
𝑃𝑜𝑢𝑡
𝑁 𝐶 𝑃, 𝑉𝑐,𝑝𝑘
10.19 [A] = 100 / (1 * 0.0981 * 100)

RF Power Amplifier Tutorial (1)

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