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 ) =
GP1P2PLF
Z1ZLF
×
j2πf + Z1
(j2πf + P1)(j2πf + P2)
×
j2πf + ZLF
j2πf + PLF

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 ) =
GP1P2PLF
Z1ZLF
×
j2πf + Z1
(j2πf + P1)(j2πf + P2)
×
j2πf + ZLF
j2πf + PLF
H( f ) =
GP1P2PLF
Z1ZLF
×
s + Z1
(s + P1)(s + P2)
×
s + ZLF
s + PLF
s = σ + j2πf

4. Poles and Zeros 3-D plot
• T
P1
P2
PLFZ1
ZLF

5. Distances
• Rewrite the equation with distances.
P1 P2
PLF
Z1 ZLF
̂Z1
dP1
dP2
dPLF
dZ1
dZLF
d ̂Z1
H( f ) =
GP1P2PLF
Z1ZLF
×
s + Z1
(s + P1)(s + P2)
×
s + ZLF
s + PLF
H( f ) = C ×
dZ1
dP1
dP2
×
dZLF
dPLF
̂ZLF
f

6. Zeros
Only the Zeros point move with different CTLE levels.
The C compensate the attenuation.
H( f ) = C ×
dZ1
dP1
dP2
×
dZLF
dPLF

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.
Z1
ΔdZ1
Z1
̂Z1
dZ1
d ̂Z1
fhigh
flow
ΔdZ1
ΔdZ1
H( f ) = C ×
dZ1
dP1
dP2
×
dZLF
dPLF

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 ) =
GP1P2PLF
Z1ZLF
×
j2πf + Z1
(j2πf + P1)(j2πf + P2)
×
j2πf + ZLF
j2πf + PLF
H( f ) =
GP1P2
Z1
×
j2πf + Z1
(j2πf + P1)(j2πf + P2)

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
Zp = 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