Post on 24-May-2015
description
Primary Mixer S-functions
An application of ICE
June 2012
© NMDG 2012 2
Outline● From S-parameters to Primary S-functions
● The Strength of Primary S-functions
● Blockdiagram and Practical Setup with Rohde & Schwarz ZVA24
● Case Study
● Comparison with “Regular” S-parameters● Up-conversion, Down-conversion functions and Interpretation
● Mixer Reciprocity
● Conclusions
© NMDG 2012 3
S-parameters
a1 a2
b1 and b2
b2
S-parameters predict reflected waves
for any given incident waves
within the measured frequency band
and as long the device behaves linear
a1 and a2
b1
© NMDG 2012 4
Primary Mixer S-functions(*)
a1
b1
a2
b2
a3 b3 Port 3: LO Port
a3L f lo Large Pumping Signal
b1 , b2 and possibly b3Primary S-functions predict reflected waves
for any given incident waves
as function of the LO pumping signal
within the measured frequency band
and as long as the nonlinear behaviour is only determined by the LO pumping signal (**)
a1 , a2 and possibly including effect of a3
(*) Patent Pending (**) This motivates the terminology “Primary”
© NMDG 2012 5
The Strength of Primary Mixer S-functions
a1
b1
b2
a3L f lo
f −kf lo± f
Up-conversionDown-conversionLeakage
Deals withexternal mismatches, inducing upconverted and downconvertedsignals in the incident waves
a2
between each port, also LO port
and vice versa
for each port, also LO port
Includesthe mixer reflectionswithin the measurement bandwidth
for each port, also LO port
© NMDG 2012 6
The Primary Mixer S-functions - Equations
bs f =S st , n f , f lo ,∣a3 f lo∣a3∣n∣s n f loa t −n f lo f
For n = 0 → regular S-parameters bs f =S st , n f at f
a3L f lo
x a3 f lo
Alternative:
Sst ,1 f , f lo ,∣a3 f lo ∣
− f lo f f
x a3− f lo Sst ,−1 f , f lo ,∣a3 f lo∣
f lo f f
with ∣n∣N and s n= sign of n
bs f =S st , n f , f lo ,∣a3 f lo∣a3 f lo∣a3 f lo∣
n
a t −n f lo f ...
For n = 1 →
For n = -1 →
“Up-conversion”
“Down-conversion”
Remark: These functions are available for s and t, equal to any port number
(*)
(*) Einstein notation
© NMDG 2012 7
Block diagram for 3-port Extraction
LO
Port1 Port2
Port3
a1
b1
a2
b2
a3b3
Small-SignalExcitation
LO Pumping Signal
Absolute calibration planes● Relative calibration● Power calibration● Phase calibration
fsteps throughRF and IF bands
f loSwitch: possibly with 50 Ohm terminations
Small-Signal Excitation: can be replaced with multi-tone generator (measurement speed)
© NMDG 2012 8
Block diagram for 2-port Extraction
LO
Port1 Port2
Port3
a1
b1
a2
b2
a3b3
Small-SignalExcitation
LO Pumping Signal
Absolute calibration planes● Relative calibration● Power calibration● Phase calibration
fsteps throughRF and IF bands
f lo
© NMDG 2012 9
Practical Setup with Rohde & Schwarz ZVA24
RF
LO IF
Phase Ref
Synchronizer
Power Sensor
LO Pumping Signal
Relative Calibration Kit
© NMDG 2012 10
Case Study
a1
b1 b2
a3
LO
7 GHz Fixed LO drive level at 10 dBm
a2Small-Signal
Excitation at ports
f
IF : DC – 3 GHzLower band : 4 GHz – 7 GHzUpper band : 7 GHz – 10 GHzLast band :11 GHz – 13 GHz
Power level at -15 dBm
RF portof test mixer
IF portof test mixer
© NMDG 2012 11
2 4 6 8 10 12freq GHz
30
25
20
15
10
5
dBS11
Regular S-parametersSst ,0 f , f lo ,∣a3 f lo∣
2 4 6 8 10 12freq GHz
35
30
25
20
15
dBS12
2 4 6 8 10 12freq GHz
45
40
35
30
25
20
15
dBS21
2 4 6 8 10 12freq GHz
15
10
5
dBS22
IF
LO
LowerBand
UpperBand
Max freq
2 LO
© NMDG 2012 12
Comparison with “Regular” S-parameters
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOO
O
OO
OO
O
OO
O
OOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
2 4 6 8 10 12freq GHz
35
30
25
20
15
10
5
dBS11
Regular(less smooth)
O
O
O
OOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
2 4 6 8 10 12freq GHz
50
40
30
20
10
dBS21
Regular(less smooth)
Impact of LO
“Regular” means thatmixer was considered assimple linear 2-port deviceand S-par were measuredafter regular relative calibration
Part of primary S-function
“Regular” S-parameter
© NMDG 2012 13
Examples of Up-conversion functions
2 4 6 8 10 12freq GHz
40
35
30
25
20
15
dBTo port 1 from port 1 flof
2 4 6 8 10 12freq GHz
50
40
30
20
10
dBTo port 1 from port 2 flof
2 4 6 8 10 12freq GHz
60
40
20
dBTo port 2 from port 1 flof
2 4 6 8 10 12freq GHz
35
30
25
20
15
dBTo port 2 from port 2 flof
S11,1 f , f Lo ,∣a3 f Lo∣ S12,1 f , f Lo ,∣a3 f Lo∣
S21,1 f , f Lo ,∣a3 f Lo∣ S22,1 f , f Lo ,∣a3 f Lo∣
© NMDG 2012 14
Interpretation of Up-conversion function
2 4 6 8 10 12freq GHz
60
40
20
dBTo port 2 from port 1 flof
S21,1 f , f Lo ,∣a3 f Lo∣
b22GHz a1−5GHz The function expresses how contributes to2GHz 10GHz
b210GHz a13GHz The function expresses how contributes to
One can apply this function to shifted by a1 f − f lo
© NMDG 2012 15
Examples of Down-conversion functions
1 2 3 4 5 6freq GHz
45
40
35
30
25
20
dBTo port 1 from port 1 flof
1 2 3 4 5 6freq GHz
50
40
30
20
10
dBTo port 1 from port 2 flof
1 2 3 4 5 6freq GHz
25
20
15
10
5dB
To port 2 from port 1 flof
1 2 3 4 5 6freq GHz
45
40
35
30
25
20dB
To port 2 from port 2 flof
S11,−1 f , f Lo ,∣a3 f Lo∣ S12,−1 f , f Lo ,∣a3 f Lo∣
S21,−1 f , f Lo ,∣a3 f Lo∣ S22,−1 f , f Lo ,∣a3 f Lo∣
© NMDG 2012 16
1 2 3 4 5 6freq GHz
25
20
15
10
5dB
To port 2 from port 1 flof
Interpretation of Down-conversion functionS21,−1 f , f Lo ,∣a3 f Lo∣
b22GHz a19GHz The function expresses how contributes to
2GHz
b25GHz a112GHz The function expresses how contributes to
One can apply this function to shifted by a1 f f lo
5 GHz
© NMDG 2012 17
Interpretation of Down-conversion function
b12GHz a19GHz The function expresses how contributes to the reflection
One can apply this function to shifted by a1 f f lo
1 2 3 4 5 6freq GHz
45
40
35
30
25
20
dBTo port 1 from port 1 flof
S11,−1 f , f Lo ,∣a3 f Lo∣
2GHz
© NMDG 2012 18
Conversion from Port 1 (RF) to Port 2 (IF)
0.5 1.0 1.5 2.0 2.5 3.0freq GHz
20
15
10
5
0dB
To port 2 from port 1 flof and flof
S21,1 f , f Lo ,∣a3 f Lo∣
S21,−1 f , f Lo ,∣a3 f Lo∣
Conversion lower side band of LO to IF
Conversion upper side band of LO to IF
f lo
(1)
(1)
(2)
(2)
© NMDG 2012 19
Mixer Reciprocity: Port 1 (RF) <> Port 2 (IF)
3 2 1 1 2 3freq GHz
10
9
8
7
6
5
dBMixer Reciprocity RF Port 1 IF Port 2
From Port 1 (RF) to Port 2 (IF)
From Port 2 (IF) to Port 1 RF)S12,1 f , f Lo ,∣a3 f Lo∣
S21,−1 f , f Lo ,∣a3 f Lo∣
From Port 1 (RF) to Port 2 (IF)S21,1 f , f Lo ,∣a3 f Lo∣
f IF :−3GHz -> 3GHzf RF :4GHz -> 10GHz
f RF :7GHz -> 10GHzf IF :DC -> 3GHz
f RF :4GHz -> 7GHzf IF :−3GHz -> DC
© NMDG 2012 20
Conclusions
● The Primary S-functions are the “S-parameters for mixers”
● Primary S-functions can predict the response of a mixer● for an arbitrary input signal within the measurement bandwidth● include the LO port, when desired● As long as the LO pumping signal is the only contributor to the nonlinearity
● Acknowledgement● Thanks to Rohde & Schwarz for providing the R&S ZVA network analyzer
equipment, the support around the network analyzer and the mixer under test
● NMDG offers the extraction of the Primary S-functions for your mixer via the NMDG measurement services
For more information info@nmdg.be
www.nmdg.be