The document discusses the definition and effectiveness of Continuous Time Linear Equalizers (CTLE) as specified in IEEE 802.3 standards. It provides a transfer function for a 50G PAM4 module and explains how altering poles and zeros affects frequency response and channel loss compensation. Key points include the relationship between zero positioning and frequency response, emphasizing CTLE’s role in mitigating channel loss.

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