Primary Mixer S-Functions Presentation

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


2 4 6 8 10 12freq GHz

60

40

20


2 4 6 8 10 12freq GHz

35

30

25

20

15


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


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


1 2 3 4 5 6freq GHz

50

40

30

20

10


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


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


Interpretation of Down-conversion functionS21,−1 f , f Lo ,∣a3 f Lo∣


2GHz


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


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 [email protected]

www.nmdg.be

Primary Mixer S-Functions Presentation

Business

Transcript of Primary Mixer S-Functions Presentation