Primary Mixer S-Functions Presentation

Primary Mixer S-functions

An application of ICE

June 2012

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 2

S-parameters

a1 a2
b1 b2

S-parameters predict reflected waves b1 and b 2
for any given incident waves a 1 and a 2
within the measured frequency band

and as long the device behaves linear

© NMDG 2012 3

Primary Mixer S-functions(*)

a1 a2
b1 b2

a3 b3 Port 3: LO Port
L
a 3  f lo  Large Pumping Signal

Primary S-functions predict reflected waves b1 , b2 and possibly b3
for any given incident waves a 1 , a 2 and possibly including effect of a 3
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 (**)

(*) (**)
Patent Pending This motivates the terminology “Primary”
© NMDG 2012 4

The Strength of Primary Mixer S-functions

Up-conversion
Down-conversion between each port, also LO port
Leakage

and vice versa

f −kf lo± f
a1 b2
b1 a2

Includes Deals with
the mixer reflections external mismatches, inducing
within the L upconverted and downconverted
a 3  f lo  signals in the incident waves
measurement bandwidth
for each port, also LO port
for each port, also LO port

© NMDG 2012 5

The Primary Mixer S-functions - Equations

b s  f =S st , n  f , f lo ,∣a 3  f lo ∣a∣3∣s n f lo a t −n f lo f  (*)
n

with ∣n∣ N and s n= sign of n

For n = 0 → regular S-parameters b s  f =S st , n  f  at  f 

For n = 1 → x a 3  f lo  S st ,1  f , f lo ,∣a3  f lo ∣

− f lo  f f “Up-conversion”

L For n = -1 → x a 3 − f lo  S st ,−1  f , f lo ,∣a 3  f lo∣
a  f lo 
3
...

f lo  f f “Down-conversion”

Remark: These functions are available for s and t, equal to any port number
n
a3  f lo 
Alternative: b s  f =S st , n  f , f lo ,∣a 3  f lo ∣  a t −n f lo f 
∣a3  f lo∣ (*)
Einstein notation
© NMDG 2012 6

Block diagram for 3-port Extraction

Small-Signal
Excitation a1 a2
Port1 Port2

f b1 b2
steps through a3 b3
RF and IF bands
Port3

Absolute calibration planes
LO
● Relative calibration
Pumping
● Power calibration
Signal
● Phase calibration
LO f lo
Switch: possibly with 50 Ohm terminations

Small-Signal Excitation: can be replaced with multi-tone generator (measurement speed)

© NMDG 2012 7

Block diagram for 2-port Extraction

Small-Signal
Excitation
a1 a2
Port1 Port2

f
b1 b2
steps through
RF and IF bands
a3 b3
Port3

LO
Pumping
Signal
Absolute calibration planes
LO f lo
● Relative calibration

● Power calibration

● Phase calibration

© NMDG 2012 8

Practical Setup with Rohde & Schwarz ZVA24

LO Pumping Signal

Synchronizer
RF
Relative Calibration Kit
IF
LO
Phase Ref

Power Sensor

© NMDG 2012 9

Case Study

RF port IF port
of test mixer of test mixer
Small-Signal
Excitation at ports a1 a2

b1 b2
f a3
Power level at -15 dBm
IF : DC – 3 GHz
Lower band : 4 GHz – 7 GHz LO
Upper band : 7 GHz – 10 GHz 7 GHz
Last band :11 GHz – 13 GHz
Fixed LO drive level at 10 dBm

© NMDG 2012 10

Regular S-parameters
S st ,0  f , f lo ,∣a 3  f lo ∣ Max freq
Lower Upper
S11
IF Band Band S12

freq GHz
dB
dB

2 4 6 8 10 12
 15
5 LO 2 LO
 20
 10

 25
 15

 20  30

 25  35

freq GHz
 30
2 4 6 8 10 12
S21
dB
S22
dB
 15

 20
5

 25

 30  10

 35

 40  15

 45
freq GHz
freq GHz 2 4 6 8 10 12
2 4 6 8 10 12

© NMDG 2012 11

Comparison with “Regular” S-parameters
S11
dB
OOOO O
OOOOOO
OOOOOOO
OOOOOO
OOO
freq GHz Part of primary S-function
OO
OO
OOO 2 4 6 8 10 12
O OO
OO
OOO
O
O
OOO OOO OO
OOOOOOOOO
OO OOOOO
OO OOOOO
OO
O OOOO
OOOO
OOOO
OOO OO
OO
OO
O OO
OO
OO
OO
O OOOOOOO
OOOOOOO
OO OOO
“Regular” S-parameter
O OOOOO
OOO OOO
OO
O O OO
5
O
OO OOOOO OOOO
OOO O OOOO
OOO
OOO OO
OO OOOOO
OOOO
OOO
OOO
O
OO
OO
OO
OO OO
OO
OO
OO
O
O OO
OO
O O
O
OO
O
O
O O
OO O
O
O
O O
OO
O O
O
O
O
O O
O
OO O
O
O O
OO O
O
O
O OO
O OO
O O O
O
 10 OO
O
O
OO
O
O
O
O
O
O O O
O
O O
O O
O
O O
OO OO
O O O
O
O OO
O OO
O O O
O O O
Regular
O O
O O O
 15 O
O O O
O O
O O
OO
O
O
O
OO
O
O
O

 20
O O
O O
O O
(less smooth)
O
O O
S21
OO
O
O
dB
Impact of LO
 25 O

freq GHz
O
O
O
O 2 4 6 8 10 12
 30 OO
O
 10
 35 OOO OO
OOO OO
OOOOO
OO
OO OOO
OOOO
OO OO
O
OO
OO
O
O OOO
OOO
OO
OO
OO
O
OO
O
O
O
OO
OO
OO
OO
O
O
O OO O
OOO
O
O O
O
OO OO OOO
O OO
OO
OO
O
O O OOO OOO
OO OOOOO
OOO
OO OOOOOO
OO OOOOOO O O
O O OO O
OOO
OO
OOO
 20 O
O
O
O
O O
OO
O OO
OO
OO
OO O
O OO O
O
O
O
OOO
OO
O
O OO OO
OO
OO OO O
O O
O
O OOOOO
OO OOO
OOOOO
OO OOO
O
O
O O
O OO
OO
O O
O O
O O
O
O O
O OO
OO
O OO O O
OO
O
O
O
O
OO O
O O
O
O
O OO
O
O
OO O
O O
O
O O
O O OO
OO O O
O O O
O O
O
O OO O O O O
O
OO O
O O
O O O
O O O O O
“Regular” means that
O
Regular
O
O O
O O
O O O
 30O O O
OO O O
O O O O
O O OO
OO
OO OO

mixer was considered as
O
(less smooth)
O OO
O
O OO OO
O
OO O
O OO
O O
OO

simple linear 2-port device
O
 40 O
O

and S-par were measured
after regular relative calibration  50 O

© NMDG 2012 12

Examples of Up-conversion functions
To port 1 from port 2  flof
dB dB

 15  10

 20
 20

 25
 30
 30
 40
 35

 40
S 11,1  f , f Lo ,∣a3  f Lo  
∣
 50
S 12,1  f , f Lo ,∣a3  f Lo ∣
freq GHz freq GHz
2 4 6 8 10 12 2 4 6 8 10 12
dB

dB
 15

 20  20

 25
 40

 30

 60

S 21,1  f , f Lo ,∣a 3  f Lo ∣
 35
S 22,1  f , f Lo ,∣a 3  f Lo ∣
freq GHz freq GHz
2 4 6 8 10 12 2 4 6 8 10 12

© NMDG 2012 13

Interpretation of Up-conversion function
S 21,1  f , f Lo ,∣a 3  f Lo ∣
dB

 20

 40

 60

freq GHz
2 4 6 8 10 12

2GHz 10GHz
The function expresses how a 1 −5 GHz  contributes to b 2 2GHz 
The function expresses how a 1 3GHz  contributes to b 2 10 GHz 

One can apply this function to a 1  f  shifted by − f lo

© NMDG 2012 14

Examples of Down-conversion functions
To port 1 from port 1  flof

dB

dB

 20
 10

 25
 20
 30

 30
 35

 40  40

 45
S 11,−1  f , f Lo ,∣a3  f Lo ∣  50

freq GHz
S 12,−1  f , f Lo ,∣a3  f Lo ∣
freq GHz
1 2 3 4 5 6
1 2 3 4 5 6

To port 2 from port 1  flof dB
dB  20
5

 25
 10

 30
 15

 35

 20
 40

 25
S 21, −1  f , f Lo ,∣a 3  f Lo ∣  45
S 22, −1  f , f Lo ,∣a 3  f Lo ∣
freq GHz
1 2 3 4 5 6 freq GHz
1 2 3 4 5 6

© NMDG 2012 15

Interpretation of Down-conversion function
S 21, −1  f , f Lo ,∣a 3  f Lo ∣
dB
5

 10

 15

 20
2GHz
 25 5 GHz

freq GHz
1 2 3 4 5 6

The function expresses how a 1 9GHz  contributes to b 2 2GHz 
The function expresses how a 1 12GHz  contributes to b 2 5 GHz 

One can apply this function to a 1  f  shifted by f lo

© NMDG 2012 16

Interpretation of Down-conversion function
S 11,−1  f , f Lo ,∣a3  f Lo ∣
dB

 20

 25

 30

 35

 40
2GHz

 45

freq GHz
1 2 3 4 5 6

The function expresses how a 1 9GHz  contributes to the reflection b1 2 GHz 

One can apply this function to a 1  f  shifted by f lo

© NMDG 2012 17

Conversion from Port 1 (RF) to Port 2 (IF)

To port 2 from port 1  flof and flof

freq GHz
dB
0
0.5 1.0 1.5 2.0 2.5 3.0

5 S 21, −1  f , f Lo ,∣a 3  f Lo ∣ (1)
Conversion upper side band of LO to IF

 10
S 21,1  f , f Lo ,∣a 3  f Lo ∣ (2)
(1)
Conversion lower side band of LO to IF
 15

 20

f lo
(2)

© NMDG 2012 18

Mixer Reciprocity: Port 1 (RF) <> Port 2 (IF)

Mixer Reciprocity  RF Port 1  IF Port 2
dB From Port 2 (IF) to Port 1 RF)
S 12,1  f , f Lo ,∣a3  f Lo ∣
From Port 1 (RF) to Port 2 (IF) 5
f IF :−3 GHz -> 3 GHz
S 21,1  f , f Lo ,∣a 3  f Lo ∣
6
f RF :4 GHz -> 10 GHz
f IF :−3 GHz -> DC 7 From Port 1 (RF) to Port 2 (IF)
S 21, −1  f , f Lo ,∣a 3  f Lo ∣
8

9
f IF : DC -> 3GHz

 10

freq GHz
3 2 1 1 2 3

© NMDG 2012 19

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
© NMDG 2012 20

Primary Mixer S-Functions Presentation

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