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59 th System LSI Joint Seminar A Novel Tri riangular Wave Slo lope Modulation for Im Improving Dynamic Perf rformance of f DC-DC Buck Converter Shu Wu Division of Electronics and Informatics School of Science and Technology Gunma

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SLIDE 1

A Novel Tri riangular Wave Slo lope Modulation for Im Improving Dynamic Perf rformance of f DC-DC Buck Converter

Shu Wu

Division of Electronics and Informatics School of Science and Technology Gunma University

59th System LSI Joint Seminar

1

slide-2
SLIDE 2

Outline

  • Background
  • Control schemes of buck converter
  • Triangular wave slope modulation
  • Circuit and principle
  • Stability analysis
  • Simulation
  • Conclusion

2

slide-3
SLIDE 3

Outline

  • Background
  • Control schemes of buck converter
  • Triangular wave slope modulation
  • Circuit and principle
  • Stability analysis
  • Simulation
  • Conclusion

3

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SLIDE 4

Background

  • Switching converter as a part of power supplies system

is very impotent for various electronic devices

(DC-DC converter, AC-DC rectifier, DC-AC inversion, AC-AC cycloconversion )

  • Two concerned issues

–Efficiency

  • Save energy
  • Control temperature (cost and stability)

–Reliability

  • Stability
  • Dynamic performance

4

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SLIDE 5

Motivation

  • Continuous advancement of integrated circuits
  • Faster and faster dynamic current slew rate (120A/us)
  • Lower and lower voltage (0.8V for subthreshold operated circuit)

Dynamic performance improvement of power supplies

  • 3 disturbance sources
  • Output reference signal
  • Input voltage
  • Load

 Band-gap reference  Line feed-forward control  Trouble

5

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SLIDE 6

Outline

  • Background
  • Control schemes of buck converter
  • Triangular wave slope modulation
  • Circuit and principle
  • Stability analysis
  • Simulation
  • Conclusion

6

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SLIDE 7

Feedback control scheme

  • -----Voltage-Mode Control

7

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SLIDE 8

Feedback control scheme

  • -----Current-Mode Control

8

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SLIDE 9

Feedback control scheme

  • -----Hysteretic Control

9

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SLIDE 10

Phase compensation for VMC and CMC

Type 2 compensator Type 3 compensator

  • Not be required in

Hysteretic control

  • Realize by the error

amplifier

  • Type 2 for CMC
  • Type 3 for VMC

10

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SLIDE 11

GBP constraint for Type 3 compensator

Type 3 :

  • Large gain at high frequency
  • Increase phase margin

Severe GBP constraint

VMC cannot has wider band (GBP---the Gain Bandwidth Product of op-amp)

11

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SLIDE 12

Advantages and Disadvantages

VMC CMC Hysteretic control

  • Easy loop analysis
  • Fixed switching frequency
  • Inherent line feed-forward
  • Wider band
  • Fixed switching frequency
  • Simple
  • Fast transient
  • No line feed-forward
  • Low bandwidth

(GBP of op-amp)

  • Current sensor
  • Slope compensation
  • Blanking time
  • Variable switching

frequency

  • Large output ripple

This research is based on VMC

The fastest The slowest

12

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SLIDE 13

Objective of this research

  • Triangular wave slope modulation
  • Based on VMC

Fixed switching frequency No require current sensor, slope compensation, and blanking time

  • The slope depends on input and output voltage

Line feed-forward control Wider band Non-linearly changed loop gain

The line and load transient response both are improved

13

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SLIDE 14

Outline

  • Background
  • Control schemes of buck converter
  • Triangular wave slope modulation
  • Circuit and principle
  • Stability analysis
  • Simulation
  • Conclusion

14

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SLIDE 15

System configuration

Op-amp1:

  • Generate control variable 𝑊

𝑑

  • Type 3 compensation

Op-amp2:

  • Amplify deviation
  • Control variable of TWG

TWG (Triangular Wave Generator): Slope adjustable

  • Controlled by 𝑊

𝑕 and 𝑊 𝑑𝑝𝑜

15

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SLIDE 16

Triangular Wave Generator (1)

VCR: Voltage Controlled Resistor VCCS: Voltage Controlled Current Source

16

Part 1 Part 2

VCR--𝑆𝐸𝑇 VCCS

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SLIDE 17
  • VCR

Triangular Wave Generator (2)---Part 1

NMOS 𝑁1 operates in triode region

Equivalent resistor:

1 𝑆𝐸𝑇 = 𝐽𝐸 𝑊𝐸𝑇 = 𝐿𝑜 𝑊 𝐻𝑇 − 𝑊 𝑢ℎ − 𝑊𝐸𝑇 2

𝑺𝑬𝑻 =

𝟐 𝑳𝒐𝑾𝒅𝒑𝒐

If 𝑆𝑐 ≫ 𝑆𝐸𝑇 𝑊

𝐸𝑇 ≈ 1 𝐿𝑜𝑆𝑐 𝑊

𝑕

𝑊

𝑑𝑝𝑜

17

Set 𝑊

𝐻𝑇 = 𝑊 𝑢ℎ + 𝑊𝐸𝑇 2 + 𝑊 𝑑𝑝𝑜 𝑆𝑐 𝑾𝒅𝒑𝒐 𝑊

𝑢ℎ

+ + +

Voltage Summer 𝑁1 VCR--𝑆𝐸𝑇 𝑾𝒉 𝑊

𝐸𝑇1

𝑆𝑐 𝑊

𝐸𝑇2

𝑁2 𝑊

𝑑_𝑛𝑏𝑦

+

  • Op-amp3

𝐻3∆𝑊

𝐸𝑇

※ 𝑳𝒐 = 𝝂𝒐𝑫𝒑𝒚𝑿 𝑴 𝑾𝒅_𝒏𝒃𝒚 = 𝑾𝒖𝒊 +

𝑾𝑬𝑻 𝟑 + 𝑾𝒅𝒑𝒐_𝒏𝒃𝒚

𝑯𝟒∆𝑾𝑬𝑻 = 𝑯𝟒𝑾𝒉 𝑳𝒐𝑺𝒄 𝟐 𝑾𝒅𝒑𝒐 − 𝟐 𝑾𝒅𝒑𝒐_𝒏𝒃𝒚

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SLIDE 18
  • VCCS & TWG

Triangular Wave Generator (3)---Part 2

𝑊

𝐸𝐸

+

Op-amp4 𝑁3 𝑁4

𝑾𝒖𝒔𝒋

CLK

VCCS

𝐷𝑑 𝑆𝑑𝑡 𝑊

𝑏

𝑊

𝑐

𝑗𝑑

𝑗𝑑𝑡 Q

𝑗𝐷 = 𝑗𝐷𝑇 =

𝑊

𝑏−𝑊𝑐

𝑆𝐷𝑇 = 𝐻3∆𝑊𝐸𝑇 𝑆𝐷𝑇

  • Op-amp5
  • +

𝑊

𝑢𝑠𝑗 = 𝑗𝑑 𝐷𝑑 𝑢

𝑊

𝑢𝑠𝑗 = 𝑏 ∙ 𝑊 𝑕 ∙ 1 𝑊

𝑑𝑝𝑜 − 𝑐 𝑢 = 𝑁 𝑊

𝑕, 𝑊 𝑑𝑝𝑜 ∙ 𝑢

18

𝐻3∆𝑊

𝐸𝑇

𝑏 = 𝐻3 𝐿𝑜𝑆𝐶𝑆𝐷𝑇𝐷𝑑 𝑐 = 1 𝑊

𝑑𝑝𝑜_𝑛𝑏𝑦

Where

𝑁 ∝ 𝑊

𝑕 , 𝑁 ∝ 1 𝑊

𝑑𝑝𝑜

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SLIDE 19

𝑊

𝑝𝑣𝑢 =

1 𝑀𝐷𝑡2 + 𝑀 𝑆 𝑡 + 1 𝑊

𝑕

𝑊

𝑄

𝑊

𝑑

Line feed-forward control (1)

Transfer function from control variable to output voltage (VMC buck converter)

19

𝑊

𝑄 --- the peak of triangular wave

𝑊

𝑕

𝑊

𝑝𝑣𝑢

𝑊

𝑑

𝑊

𝑝𝑣𝑢

Conventional VMC: Output voltage return to the reference

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SLIDE 20

Line feed-forward: 𝑊

𝑕

𝑊

𝑞 = 𝑁 𝑊 𝑕, 𝑊 𝑑𝑝𝑜 ∙ 𝑈 𝑡 =

1 𝑊

𝑑𝑝𝑜 −

1 𝑊

𝑑𝑝𝑜_𝑛𝑏𝑦 𝐻3𝑈 𝑡

𝐷𝐷𝑆𝐷𝑇𝑆𝑐𝐿𝑜 ∙ 𝑊

𝑕

𝑊

𝑄

The input variation is eliminated by the proportional variation in 𝑊

𝑄

Nothing to do with 𝑊

𝑝𝑣𝑢 and 𝑊 𝑑

Line feed-forward control (2)

*The changed 𝑊

𝑕 cause the ripple of inductor current is changed

During line transient response, 𝑱𝑴 ≠ 𝑱𝒑𝒗𝒖. Similar to load transient response

Line feed-forward only consider the input voltage variation

20

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SLIDE 21

∆𝑒1 = 𝑊

𝐷

𝑈

𝑡

∙ 1 𝑛2 − 1 𝑛1 = 𝑊

𝐷

𝑈

𝑡

∙ ∆ 1 𝑛 ∆𝑒2 = 𝐻𝑑∆𝑤 𝑈

𝑡

∙ 1 𝑛2 = 𝐻𝑑∆𝑤 𝑈

𝑡

∙ 1 𝑛1 + ∆ 1 𝑛

Once output voltage deviate from the reference, whatever the reason ∆𝑒1 is caused by slope modulation ∆𝑒2 is caused by slope and 𝑾𝒅 modulations

∆𝒆 = ∆𝒆𝟐 + ∆𝒆𝟑= 𝑾𝑫 + 𝑯𝒅∆𝒘 𝑼𝒕 ∙ ∆ 𝟐 𝒏 + 𝑯𝒅∆𝒘 𝑾𝒒_𝒕𝒕 Conventional VMC Additional duty cycle modulation by proposed TWG

21

𝑊

𝑞_𝑡𝑡 = 𝑛1𝑈 𝑡

Non-linear duty cycle modulation(1)

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SLIDE 22

Non-linear duty cycle modulation(2)

∆𝑒 ∆𝑤 = A ∆𝑤 ∙ ∆𝑤 + 𝐻𝑑∆𝑤 𝑊

𝑞_𝑡𝑡

A ∆𝑤 = 𝑊

𝐷 + 𝐻𝑑∆𝑤 𝐻𝑙

𝑈

𝑡 ∙ 𝑏 ∙ 𝑊 𝑕 𝑐 𝑊 𝑠𝑓𝑔 − 𝐻𝑙∆𝑤 − 1 ∙ 𝑐𝑊 𝑠𝑓𝑔 − 1

∆𝑤

Large Large approach to 0

A ∆𝑤

approach to a constant

Non-linearly change Enable fast transient response To ensure the loop stability

A 0 = 𝑊

𝐷𝐻𝑙

𝑈

𝑡 ∙ 𝑏 ∙ 𝑐𝑊 𝑠𝑓𝑔 − 1 2

22

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SLIDE 23

Outline

  • Background
  • Control schemes of buck converter
  • Triangular wave slope modulation
  • Circuit and principle
  • Stability analysis
  • Simulation
  • Conclusion

23

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SLIDE 24

System block diagram

𝑈 𝑡 = 𝐵 0 + 𝐻𝑑 𝑡 𝑊

𝑞_𝑡𝑡

∙ 𝐼 𝑡 ∙ 𝐻𝑤𝑒 𝑡 𝑈 𝑡 = 𝐵 0 ∙ 𝐼 𝑡 ∙ 𝐻𝑤𝑒 𝑡 + 𝐼 𝑡 𝐻𝑑 𝑡 𝐻𝑤𝑒 𝑡 𝑊

𝑞_𝑡𝑡

A 0 = 𝑊

𝐷𝐻𝑙

𝑈

𝑡 ∙ 𝑏 ∙ 𝑐𝑊 𝑠𝑓𝑔 − 1 2

Conventional VMC

24

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SLIDE 25

Bode plot

Buck converter with conventional VMC: 𝑔

𝑑 =

𝑔

𝑡 20 = 50𝑙𝐼𝑨, 𝜒𝑛 = 40°

TWG: 𝐵 0 ≈ 6.65 Compared to conventional VMC

  • -- (𝐻𝑑𝐻𝑤𝑒/𝑊

𝑞)

  • Bandwidth increase

50kHz  68kHz

  • Phase margin decrease

40° 17 ° Oscillation, even unstable

25

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SLIDE 26

Nyquist plot

In order to get enough phase margin Method 1: Increase the high-frequency phase of 𝐻𝑑 𝑡 𝐻𝑤𝑒 𝑡 𝑊

𝑞_𝑡𝑡

Method 2: Increase the high-frequency phase of 𝐵 0 𝐻𝑤𝑒 𝑡

26

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SLIDE 27

Two methods for enough phase margin

Method 1 Method 2

  • Crossover frequency decrease 
  • Impossible (GBP of op-amp1)

  • Crossover frequency increase 
  • Easy 

Add a high-frequency zero in TWG TWG phase compensation

27

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SLIDE 28

TWG phase compensation

𝐻6 𝑡 = 𝑆2 𝑆1 𝐷1𝑆1𝑡 + 1

𝒈𝒅 = 𝟗𝟓𝒍𝑰𝒜 𝝌𝒏 = 𝟒𝟗°

28

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SLIDE 29

Outline

  • Background
  • Control schemes of buck converter
  • Triangular wave slope modulation
  • Circuit and principle
  • Stability analysis
  • Simulation
  • Conclusion

29

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SLIDE 30

Simulation condition

Simulator: SIMetrix 6.2

Buck converter Type 3 compensator TWG

𝑊

𝑕 = 5𝑊

𝑊

𝑝𝑣𝑢 = 3.5𝑊

𝑊

𝑞_𝑡𝑡 = 3𝑊

𝑀 = 10𝜈𝐼 𝐷 = 50𝜈𝐺 𝑆 = 35𝛻 𝑆𝐹𝑇𝑆 = 2𝑛𝛻 𝑆′ = 50𝑛𝛻 𝑔

𝑡 = 1𝑁𝐼𝑨

Power loss elements: 𝑆′ = 𝑆𝑀 + 𝐸𝑆𝑝𝑜 + 𝐸′𝑆𝐸

Compensation Goal 𝑔

𝑑 =

𝑔

𝑡 20 = 50𝑙𝐼𝑨

𝜒𝑛 = 40° Error Amplifier 𝐻𝑝𝑞𝑓𝑜−𝑚𝑝𝑝𝑞 = 100𝑙 𝐻𝐶𝑄 = 20𝑁𝐼𝑨 Realization

𝑆1 = 10𝑙𝛻 𝑆2 = 9𝛻 𝑆3 = 10.6𝑙𝛻 𝐷1 = 180𝑞𝐺 𝐷2 = 11.2𝑜𝐺 𝐷3 = 647𝑞𝐺

𝐻k = 100 𝐻3 = 200 𝐿𝑜 ≈ 2 𝑆𝑐 = 1𝑙Ω 𝑆𝐷𝑇 = 330Ω 𝐷𝐷 = 300𝑞𝐺 𝑊

𝑢ℎ = 0.9𝑊

𝑊

𝑑𝑝𝑜_𝑛𝑏𝑦 = 1𝑊

𝜕ℎ𝑨 = 2𝜌 ∙ 100𝑙𝐼𝑨

𝐵 0 ≈ 6.65 𝜕ℎ𝑨: high frequency zero

30

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SLIDE 31

Line transient response (1-1)

Stepwise Change 𝑊

𝑕:

5V ⟷ 6𝑊

C-VMC: conventional voltage-mode control SATWG-VMC: voltage-mode control with slope adjustable triangular wave generator

52mV

C-VMC: 𝑊

𝑞𝑞 = 52𝑛𝑊

Step-up: 400𝜈𝑡 Step-down: 300𝜈𝑡 SATWG-VMC: No distinct change

31

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SLIDE 32

Line transient response (1-2)

𝑊

𝑕: 5V → 6V

C-VMC: 𝑊

𝑝𝑣𝑢 increase

𝑊

𝑑

decrease SATWG-VMC: 𝑊

𝑄 increase

𝐸𝑓𝑑𝑠𝑓𝑏𝑡𝑓𝑒 𝑊

𝑑

𝐺𝑗𝑦𝑓𝑒 𝑊

𝑞

= 𝑊

𝑝𝑣𝑢

𝐽𝑜𝑑𝑠𝑓𝑏𝑡𝑓𝑒 𝑊

𝑕

𝑉𝑜𝑑ℎ𝑏𝑜𝑕𝑓𝑒 𝑊

𝑑

𝐽𝑜𝑑𝑠𝑓𝑏𝑡𝑓𝑒 𝑊

𝑞

= 𝑊

𝑝𝑣𝑢

𝐽𝑜𝑑𝑠𝑓𝑏𝑡𝑓𝑒 𝑊

𝑕

32

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SLIDE 33

Line transient response (2-1)

Stepwise Change 𝑊

𝑕:

5V ⟷ 6𝑊

FF-VMC: Voltage-mode control with conventional line feed-forward control SATWG-VMC: voltage-mode control with slope adjustable triangular wave generator FF-VMC: 𝑊

𝑞𝑞 = 6𝑛𝑊

Step-up: 300𝜈𝑡 Step-down: 200𝜈𝑡 SATWG-VMC: No distinct change

33

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SLIDE 34

Line transient response (2-2)

𝑱𝑴 ≠ 𝑱𝒑𝒗𝒖

FF-VMC:

  • Only consider

the variation in 𝑊

𝑕

  • Cannot detect

the variation in 𝑊

𝑝𝑣𝑢

Cause variation in output voltage

SATWG-VMC:

𝑊

𝑕 and 𝑊 𝑝𝑣𝑢

are both considered.

The slope get further regulation by the variation in 𝑊

𝑝𝑣𝑢

𝑊

𝑕: 5V → 6V

34

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SLIDE 35

Line transient response (3-1)

Periodic Change 𝑊

𝑕:

5V + 0.1sin(2𝜌 ∙ 1𝑙𝐼𝑨 ∙ 𝑢)

Input: 𝑊

𝑞𝑞 = 200𝑛𝑊

C-VMC: 𝑊

𝑞𝑞 = 4𝑛𝑊

FF-VMC: 𝑊

𝑞𝑞 = 2𝑛𝑊

SATWG-VMC: 𝑊

𝑞𝑞 = 0.15𝑛𝑊

35

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SLIDE 36

Line transient response (3-2)

Periodic Change 𝑊

𝑕:

5V + 0.1sin(2𝜌 ∙ 10𝑙𝐼𝑨 ∙ 𝑢)

Input: 𝑊

𝑞𝑞 = 200𝑛𝑊

C-VMC: 𝑊

𝑞𝑞 = 6.5𝑛𝑊

FF-VMC: 𝑊

𝑞𝑞 = 2.9𝑛𝑊

SATWG-VMC: 𝑊

𝑞𝑞 = 0.16𝑛𝑊

36

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SLIDE 37

Load transient response (1-1)

Stepwise Change 𝐽𝑝𝑣𝑢: 100m𝐵 ⟷ 400𝑛𝐵

C-VMC: 𝑊

𝑞𝑞 = 30𝑛𝑊

Step-up: 16𝜈𝑡 Step-down: 22𝜈𝑡 SATWG-VMC: 𝑊

𝑞𝑞 = 16.5𝑛𝑊

Step-up: 6𝜈𝑡 Step-down: 8𝜈𝑡

37

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SLIDE 38

Load transient response (1-2)

𝐽𝑝𝑣𝑢: 100mA → 400mA

C-VMC: Only 𝑊

𝑑 modulates the duty cycle

SATWG-VMC: 𝑊

𝑑 and triangular wave

regulate the duty cycle

Inductor current rise straight 8mV is the minimum undershoot

38

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SLIDE 39

Load transient response (2-1)

Using a wideband op-amp to design type 3 compensator for conventional VMC, Set crossover frequency at 𝑔

𝑡 20,

𝑔

𝑡 10 and

𝑔

𝑡 5; phase margin 𝜒𝑛 = 50°

GBP=20MHz GBP=1GHz Normal op-amp Wideband op-amp

39

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SLIDE 40

Load transient response (2-2)

Dynamic performance ranking Stepwise Change 𝐽𝑝𝑣𝑢: 100m𝐵 ⟷ 400𝑛𝐵

100m𝐵 → 400𝑛𝐵 400m𝐵 → 100𝑛𝐵

Under shoot Time

  • ver

shoot Time

SATWG 𝒈𝒕 𝟔 𝒈𝒕 𝟐𝟏 𝒈𝒕 𝟑𝟏 SATWG 𝒈𝒕 𝟔 𝒈𝒕 𝟐𝟏 𝒈𝒕 𝟑𝟏 𝒈𝒕 𝟔 𝒈𝒕 𝟔 SATWG 𝒈𝒕 𝟐𝟏 SATWG 𝒈𝒕 𝟐𝟏 𝒈𝒕 𝟑𝟏 𝒈𝒕 𝟑𝟏

SATWG is comparable with 𝒈𝒕 𝟔 VMC, but only require a normal op-amp

40

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SLIDE 41

Load transient response (3-1)

Improved Hysteretic control in [1]

[1] M. Lin, T. Zaitsu, T. Sato and T. Nabeshima, “Frequency Domain Analysis of Fixed On-Time with Bottom Detection Control for Buck Converter”, IEEE IECON2010, pp. 475-479.

  • Fixed On-time:

almost constant switching frequency

  • Ripple injection:

small output voltage ripple Simulation conditions 𝑆𝑔 = 500𝑙𝛻 𝐷

𝑔 = 2𝑜𝐺

𝐷𝑐 = 1𝑜𝐺 𝑈

𝑝𝑜 = 200𝑜𝑡

𝑈𝑝𝑔𝑔_𝑛𝑗𝑜 = 1𝑜𝑡 𝑔

𝑡 ≈ 3.5𝑁𝐼𝑨 (𝑡𝑢𝑓𝑏𝑒𝑧 𝑡𝑢𝑏𝑢𝑓) ※ 𝑾𝒉, 𝑾𝒑𝒗𝒖, L, C and R are the same as P30

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SLIDE 42

Load transient response (3-2)

Stepwise Change 𝐽𝑝𝑣𝑢: 100m𝐵 ⟷ 400𝑛𝐵

Simulation comparison

Hysteretic control (SATWG-VMC) 𝐽𝑝𝑣𝑢: 100𝑛𝐵 → 400𝑛𝐵 Under-shoot: 8mV (8mV) Response time: 9μs (6μs) Frequency: 3.1M~5MHz (Fixed 1MHz) 𝐽𝑝𝑣𝑢: 400𝑛𝐵 → 100𝑛𝐵 Over-shoot: 4mV (8mV) Response time: 6μs (11μs) Frequency: 1M~3.8MHz (Fixed 1MHz)

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SLIDE 43

Outline

  • Background
  • Control schemes of buck converter
  • Triangular wave slope modulation
  • Circuit and principle
  • Stability analysis
  • Simulation
  • Conclusion

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SLIDE 44

Conclusion

  • Slope adjustable triangular wave
  • Slope is regulated by input voltage and output voltage
  • Provide line feed-forward control and non-linear duty cycle

modulation for VMC

  • Simulation prove the effectiveness

– Line transient response is improved, and better than conventional line feed-forward control – Load transient response is improved. Result is comparable with wide band VMC buck converter (𝑔

𝑑 =

𝑔

𝑡 5) and hysteretic control,

but only require a normal op-amp and has fixed switching frequency.

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SLIDE 45

Thanks for you attention and comments !

The End

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SLIDE 46

Q&A

  • Q1: Compare to the other method, how about the efficiency of the

proposed method A: In my research, I do not consider the efficiency problem. Normally, CMC control requires current sensor which will cause more power loss than VMC. However, in the proposed method, we add some op-amp, it is hard to say whose power loss is larger. In different application and conditions, I think the comparison result is also different. Even if compare to the simplest control scheme---Hysteretic control which only need a comparator. The switching frequency is unfixed and high, it can save the energy which is dissipated on current sensor and op-amp. But it maybe cause more switching loss.

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SLIDE 47
  • Q2: The triangular wave slope is constant in one period?

A: Under the steady state, the slope is constant, and the voltage Vtri linear increase. But during the transient response, since the current which is used the capacitor Cc has a large change, the slope should change during one period.

  • VMC and CMC, you think which one is better?

A: CMC use Type 2 compensator, and always has enough phase margin, so that its bandwidth can be designed as wider than VMC. And CMC has a inherent line feed-forward control. Therefore, considering the dynamic performance, the CMC is better. But CMC require current sensor, slope compensation, and so on. And the double feedback loop configuration is hard to analyze. It is why I try to improve the dynamic performance of VMC, VMC is simpler than CMC (except that the Type 3 compensator is more complicated than Type 2)

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