2.4 單元模式介紹
2.4.1 放大器 (Amplifier)及衰減器(Attenuator)
放大器通常採用三階非線性模型，其轉移函數如下式：
vo  k1vi  k2 vi 2  k3vi 3
(2.36)
其中 v0 (t ) 為輸出電壓 ，vi (t ) 為輸入電壓。此轉換模型只適用於弱非線性(weak
nonlinearity)電路，換句話說，當輸入功率小於 1dB 壓縮點，此三階非線性模
型可以適用。另外，此轉換模型並未考慮 VSWR 及相位特性。
衰減器通常採用的模型與放大器類似，所不同的是其增益(dB)小於零。
其雜訊指數等於它的衰減量。
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2.4.2 濾波器 (Filter)
Filters are the most fundamental building blocks for achieving frequency
selection, transmitting certain frequencies without attenuation while rejecting
other frequencies.
The basic tradeoff in filter design is low VSWR in the passband and
sufficient attenuation in the stopband.
The majority of filters achieve frequency selection by reflection; a small
class of filters called diplexers or absorptive filters achieve attenuation by
absorbing the incoming energy while presenting a good impedance match in both
passband and stopband.
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Network Analyzer
47nH
47nH
SAW
Filter
5pF
Fig 2.20
5pF
網路分析儀量測 280MHz 濾波器實例[9]
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...bpf_280MHznew..S(2,1))
...bpf_280MHznew..S(1,1))
m1
0
-10
m2
-20
-30
-40
250
260
270
280
290
300
freq, MHz
m2
freq=280.9MHz
dB(bpf_280MHznew..S(1,1))=-21.606
Fig 2.21
310
0
-20
-40
-60
-80
250
260
270
280
290
300
310
freq, MHz
m1
freq=279.7MHz
dB(bpf_280MHznew..S(2,1))=-2.783
280MHz 帶通濾波器量測：返回損耗、插入損耗 [9]
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Filters with very steep transition bands have the largest group delay, and,
conversely, flat group delay requires very gentle transition from passband to
stop-band (Gaussian => Bessel => Butterworth => Chebyshev => Elliptic).
SAW resonators filters and some digital filter implementations avoid this
difficulty and can shape the amplitude and phase responses independently.
Crystal filters are used whenever very narrow bandpass filters are
required, such as in receiver IF stages for adjacent channel rejection, in SSB
systems for sideband rejection, and following oscillator stages for noise
attenuation. They are low-frequency devices, limited to less than 200 MHz.
The main advantages of passive filters are their immunity from
inter-modulation (IM) distortion and their simple tradeoff between insertion
loss and physical size; the intercept points and noise figures of active devices are
not as easy to change to suit system requirements.
The main advantage of active filters at low frequencies is that inductors are
not required in their implementation.
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Butterworth 型 –
參數包括：置入損失(insertion loss)，中心頻率，3-dB 頻寬，最大衰減值
z-dB 及共振器(resonators)的個數 n。
The Butterworth filter response is described by:
A(dB)  10 log10 (1  k 2n )
(2.37)
where k  bx / b3 for bandpass filter, b3 is the 3 dB bandwidth of the filter and
bx is the bandwidth at the frequency x ( bx  | x  fc | ).
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Output power spectrum (Butterworth filter, n=5)
-20
-40
-60
-80
-100
-120
0
100
200
300
400
500
600
frequency (MHz)
group delay
700
800
900
1000
20
ns
15
10
5
0
200
250
300
350
frequency (MHz)
400
450
500
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Chebyshev 型 –
參數包括：置入損失(insertion loss)，中心頻率，3-dB 頻寬，最大衰減值
z-dB，鏈波(ripple)比及共振器(resonators)的個數 n。
The Chebyshev filter response is described by:
A(dB)  10 log10 [1  (10 Amax /10  1)cosh 2 [n cosh 1 (k )]]
(2.38)
where Amax is the ripple in dB, k  bx / b3 for bandpass filter, b3 is the 3 dB
bandwidth of the filter and bx is the bandwidth at the frequency x
( bx  | x  fc | ).
The sharpness of the response is a function of the value of n and ripple. As
these values increase, the shape factor is reduced and approaches.
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Output power spectrum (Chebyshev filter, A=.5 dB n=4)
0
-50
-100
0
500
1000
1500
frequency (MHz)
group delay
25
20
ns
15
10
5
0
800
820
840
860
880
900
920
frequency (MHz)
940
960
980
1000
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2.4.3 混波器-本地振盪器 (Mixer-Oscillator)
混波器與本地振盪器通常採用合併的模型。
參數包括：置入損失(insertion loss)，本地振盪器之輸出功率及頻率，寬
頻雜訊(wide-band noise)，混波器之 MNB(mixer noise balance)，注入濾波器在
距離一個中頻頻率處之衰減量，雜訊指數(noise figure) ，4 x 6 mixer spur chart
及得到此表格時之射頻輸入功率(盡可能小於基頻之 1-dB 壓縮點)。
再加上本地振盪器之相位雜訊，即距離 f x MHz 處之相對本地振盪器輸
出功率的大小(dBc/Hz)，通常 f 可為 0.1 MHz 或 0.01 MHz。
model:
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y (t )   (k i 0  k i1v(t )  k i 2 v 2 (t )  k i 3 v 3 (t ))  cos((i  1) wt )
i 1
(2.39)
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Mixer : mimi-circuit RMS-2
fR*0
fR*1
fR*2
fR*3
99
26
34
45
fL*0
26
7.5
49
36
fL*1
25
41
32
49
fL*2
61
24
57
38
fL*3
Decay Matrix
50
39
42
73
fL*4
Si(t)
41
49
54
45
fL*5
S0(t)
LO *1 *2 *3
*4 *5
Fig 2.22 混波器與本地振盪器示意圖
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EX: (a)試說明混波器的功能( 0  m, n  5 )。(b)假設 f RF  5.7GHz 及
f LO  5.1GHz ，是否可能輸出 9.6GHz？為什麼？
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