Understanding CTLE

Understanding the math of CTLE definition in IEEE 802.3 which used by 50G PAM4 ( 200GAUI-4/400GAUI-8)

1. Understanding CTLE
Jeffrey.Wang
2019.8.3

2. Definition
•CTLE used by 50G PAM4 module is defined in 802.3 120E.3.1.7.
H(f)=
GP
1
P
2
P
LF
Z
1Z
LF
×
j2πf+Z
1
(j2πf+P
1)(j2πf+P
2)
×
j2πf+Z
LF
j2πf+P
LF

3. Idea
•This transfer function comes from $ domain transfer
function with $ .
•The $ domain transfer function is:
•Plot the $ domain with CTLE level 3.5dB.(Next page)
s
σ=0
s
s
H(f)=
GP
1
P
2
P
LF
Z
1Z
LF
×
j2πf+Z
1
(j2πf+P
1)(j2πf+P
2)
×
j2πf+Z
LF
j2πf+P
LF
H(f)=
GP
1
P
2
P
LF
Z
1Z
LF
×
s+Z
1
(s+P
1)(s+P
2)
×
s+Z
LF
s+P
LF
s=σ+j2πf

4. Poles and Zeros 3-D plot
•T
!P
1
!P
2
!P
LF!Z
1
!Z
LF

5. Distances
•Rewrite the equation with distances.
!P
1
!P
2
!P
LF
!Z
1
!Z
LF
!̂Z
1
!d
P
1
!d
P
2
!d
P
LF
!d
Z
1
!d
Z
LF
!d̂Z
1
H(f)=
GP
1
P
2
P
LF
Z
1Z
LF
×
s+Z
1
(s+P
1)(s+P
2)
×
s+Z
LF
s+P
LF
H(f)=C×
d
Z
1
d
P
1
d
P
2
×
d
Z
LF
d
P
LF
!̂Z
LF
!f

6. Zeros
Only the Zeros point move with different CTLE levels.
The C compensate the attenuation.
H(f)=C×
d
Z
1
d
P
1
d
P
2
×
d
Z
LF
d
P
LF

7. Zeros
Let’s look at the distance with !.
Since ! is larger at low frequency than at high frequency, the output of
transfer function will decrease more at low frequency.
Z
1
Δd
Z
1
!Z
1
!̂Z
1
!d
Z
1
!d̂Z
1
!f
high
!f
low
!Δd
Z
1
!Δd
Z
1
H(f)=C×
d
Z
1
d
P
1
d
P
2
×
d
Z
LF
d
P
LF

8. Result
Cut the surface at ! , we’ll get the frequency response.σ=0
Cross section
at !σ=0
Keep positive
frequency and plot in
logarithmic scale

9. Comparison
•50G PAM4 CTLE 120E.3.1.7. (Green in the diagram)
•25G NRZ CTLE 83E.3.1.6.1. (Red in the diagram)
H(f)=
GP
1
P
2
P
LF
Z
1Z
LF
×
j2πf+Z
1
(j2πf+P
1)(j2πf+P
2)
×
j2πf+Z
LF
j2πf+P
LF
H(f)=
GP
1
P
2
Z
1
×
j2πf+Z
1
(j2πf+P
1)(j2πf+P
2)

10. Effectiveness
•IEEE 802.3 120E.3.2.1.1 defined the worst case channel
loss. Used the channel loss definition in 92.10.7.1.1 with
$Z
p=151mm

11. Effectiveness(cont.)
•See the following diagram for the combination of CTLE
and channel loss.
CTLE
channel loss
combine

12. Summary
•Choose different poles and zeros can get different
surface in $ domain.
•Move the zeros to origin will will get more attenuation at
low frequency than at high frequency.
•CTLE may vary with different standards, but the idea is
the same.
•The effectiveness of CTLE is to compensate the channel
loss.
s