Post on 03-Feb-2021
The Weaver SSB Architecture
ES442 – Lecture 6.5
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-‐π/2 Σ-‐π/2 m (t)
LPF
LPF
Audio Input
Audio Subcarrier
LO1 LO2 Carrier
SSB Out
Introduc>on to Weaver Architecture
1. Known as the “third method” for generaEng SSB signals 2. Introduced in 1956 by Donald Weaver (in the Proc. IRE) 3. Used now mostly in digital communicaEon systems 4. Uses four mixers – greater complexity 5. Depends upon the selecEvity of the low-‐pass filters
2
D.K. Weaver, “A third method of generaEon and detecEon of single-‐sideband signals,” Proc. of IRE, 1956; pp. 1903-‐5. M.K. Parekkat & D.D. Krishna, “On the VisualizaEon of the Weaver’s “Third Method” for SSB GeneraEon,” IETE J. of Educa>on, Vol. 56, No. 1, 2015; pp. 28-‐33.
Uses quadrature signals generated at fixed frequencies rather than generaEng wideband quadrature phase shies as used in the phase shie method of SSB generaEon.
( )
1 2 3
( ) is band-‐limited to , where 2 ( Hz)2
We define and . The LPF = B.2
a b b a
C dB
m t B BB B B
ω ω ω ω ω π
πω π ω ω π ω π
≤ ≤ − =
= = = ±
-‐π/2 Σ
cos(ω2t)
sin(ω2t)
+
-‐π/2
cos(ω1t)
sin(ω1t)
m (t)
m(t)
m (t) ( )SSB fϕ ±
LPF
LPF
±
B
C
D F
E G
ω1 = πB ω2 = ωC ± πB B Hz H
A
Weaver Modulator for SSB
3
Mixing Products
RF Signal LO Signal Mixing Products as Output
m(t)cos(ωCt) cos(ωLOt)
½m(t)⋅[ cos(ωCt -‐ωLot) + cos(ωCt +ωLot) ]
m(t)sin(ωCt)
cos(ωLOt)
½m(t)⋅[ sin(ωCt -‐ωLot) + sin(ωCt +ωLot) ]
m(t)cos(ωCt)
sin(ωLOt)
½m(t)⋅[ - sin(ωCt -‐ωLot) + sin(ωCt +ωLot) ]
m(t)sin(ωCt)
sin(ωLOt)
½m(t)⋅[ cos(ωCt -‐ωLot) -‐ cos(ωCt +ωLot) ]
4
The Mathema>cs of the Weaver SSB Generator
5
1 2 3
12
Modulating signal ( ) is band-‐limited at Hz ( 2 radians/sec).2Define and . The LPF is B.2
At the first mixer we have:
Upper branch: cos( ) cos( ) cos( ) cos(
m
C dB
m m m
m t B BB B B
t Bt Bt t Bt t
ω π
πω π ω ω π ω π
ω π π ω π ω
=
= = = ±
⋅ = − + +[ ][ ]
[ ][ ]
12
1212
)
Lower branch: cos( ) sin( ) sin( ) sin( )
Performing the low-‐pass filter operation:
LPF upper branch gives cos( ) , and
LPF lower branch gives: sin( )
Next we pass the
m m m
m
m
t Bt Bt t Bt t
Bt t
Bt t
ω π π ω π ω
π ω
π ω
⋅ = − + +
−
−
[ ] [ ]
[ ]
2
2 2
2
2 2
12
1 14 4
12
1 14 4
filtered signals to the second mixer in each branch.
Upper branch: cos( ) cos( )
cos( ( ) ) cos( ( ) ) , and
Lower branch: sin( ) sin( )
cos( ( ) ) cos( (
m
m m
m
m
Bt t t
B t B t
Bt t t
B t B
π ω ω
ω π ω ω π ω
π ω ω
ω π ω ω π
− ⋅ =
+ − + − −
− ⋅ =
+ − − −[ ]) )Adding both mixer outputs gives USSB, while subtracting gives LSSB.
m tω−
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Real
A
Real
B
Real
D
Real
F
2πB
-‐2πB
πB
-‐πB
πB
-‐πB
3πB
-‐3πB -‐ωC
-‐(ωC+πB)
ωC (ωC+πB)
cos[(ωC±πB)t] cos(πBt)
sin(πBt)
LPF
LPF
±
B
C
D F
E G
A H
sin[(ω2±πB)t]
ω3dB = πB
ω3dB = πB
Envisioning the Opera>on of the Weaver SSB Generator – I
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Envisioning the Opera>on of the Weaver SSB Generator – II
Real
A
Real
C
Real
E
Real
G
2πB
-‐2πB
πB -‐πB
πB -‐πB
3πB
-‐3πB
-‐ω2
-‐(ω2+πB)
ω2
(ω2+πB)
cos[(ωC±πB)t] cos(πBt)
sin(πBt)
LPF
LPF
±
B
C
D F
E G
A H
sin[(ω2±πB)t]
ω3dB = πB
ω3dB = πB
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Envisioning the Opera>on of the Weaver SSB Generator – III
Real
G
H = F + G
Real
Real
F
H = F -‐ G
Real
-‐ω2
-‐(ω2+πB)
ω2 (ω2+πB)
-‐ω2
-‐(ω2+πB)
ω2
(ω2+πB)
-‐ω2
-‐(ω2+πB)
ω2 (ω2+πB)
-‐ω2
-‐(ω2+πB)
ω2 (ω2+πB)
cos[(ωC±πB)t] cos(πBt)
sin(πBt)
LPF
LPF
±
B
C
D F
E G
A H
sin[(ω2±πB)t]
ω3dB = πB
ω3dB = πB
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( )
1 2 3
( ) is band-‐limited to , where 2 ( Hz)2
We define and . The LPF = B.2
a b b a
C dB
m t B BB B B
ω ω ω ω ω π
πω π ω ω π ω π
≤ ≤ − =
= = = ±
-‐π/2 Σ
cos(ω1t)
sin(ω1t)
+
-‐π/2
cos(ω2t)
sin(ω2t)
m (t) ( )SSB fϕ ±
LPF
LPF
±
B
C
D F
E G
B Hz ω2 = ωC ± πB ω1 = πB
H
A
Weaver SSB Demodulator (Receiver)
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( ) ( )( ) ( ) cos ( ) sin , where( ) ( ) cos( ( ))( ) ( ) sin( ( ))
I C Q C
I
Q
m t m t t m t tm t m t tm t m t t
ω ω
φ
φ
= ⋅ − ⋅
= ⋅
= ⋅
Inphase
Quadrature
Phasor of m(t)
mI(t)
mQ(t)
( )tφ
Expressing Signals in I-‐Q Format
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Genera>ng Quadrature Signals
-‐π/2 m(t)
cos(ωct)
sin(ωct)
mI (t)
mQ(t)
LPF
LPF
Oscillator Input
GeneraEng mI (t) and mQ(t) quadrature signals
I-‐Q Modulator
12
Quadrature Signal Demodula>on
-‐π/2
g(t) Σ
cos(ωct)
sin(ωct)
mI (t)
mQ(t)
+
Oscillator
13
Quadrature Amplitude Modula>on (QAM)
16-‐QAM
14
Transceiver Block Diagram (LTE Handset Radio)
Filter
TX
RX
DSP PR
OCE
SSOR
Filter
Filter
PLL TCXO
Frequency Synthesizer
Mixer
Mixer
Filter
Σ 0 -‐90
0 -‐90
Filter
Q
Q
I
I
LO DistribuEon Amplifiers
LNA
Power Amplifier
Filter
Filter
Switch (Duplexer)
A/D
A/D
D/A
D/A
Antenna
15
Op>onal Slides
16
Ways to Construct a Balun (Balanced-‐to-‐Unbalanced)
A B
C
D G
G
DifferenEal Output
A
B
C
D
GG
A B
C GG
D
Center-‐Tapped Transformer
Trifilar-‐Wound Toroid Flat layout Interwound