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Hi everyone, this is Shuilin Tian.
Today I will introduce you a unified equivalent circuit model of V2 control
which is also applicable to ripple based control
The equivalent circuit model can predict all transfer functions accurately up to half of switching frequency
This model is applicable to all kinds of capacitors and to different modulation schemes
Such as constant on time V2 control and constant frequency V2 control
Hopefully this model will serve as a powerful tool for understanding and designing purpose.
First, let me give a brief introduction of V2 control.
The output voltage is fedback and used twice.
one through a direct feedback without any compensation
The other comes through a simple integrator to provide control signal
In many applications, the outer loop integrator can also be saved, which is called ripple based control
This structure is very simple and provides very fast transient response
It is widely used in industry: Many products employs constant on time V2 control or constant frequency V2 control schemes.
The issue for this structure is that the stability is related with capacitor parameters
as the output voltage contains ESR ripple and capacitor voltage ripple
For large ESR capacitors such as OSCON Caps, ESR ripple is dominant and this structure is elegant
However, for small ESR capacitors such as ceramic caps, capacitor voltage feedback is strong and instability is observed
Industry products use additional inductor current feedback to stabilize the circuit
Alternatively, capacitor company such as TDK provides some series of controlled ESR ceramic Caps
letting customers customize ESR of the Ceramic Caps to stabilize the circuit
For understanding and designing purpose
it is wonderful if a simple small-signal equivalent circuit model is developed
In this graph output voltage is separated into inductor current feedback, capacitor voltage feedback and load current feedback
The new challenge for modeling V2 control is that
not only inductor current ripple participate modulation, but also the capacitor voltage ripple
As a result, if there is modulation on control signal
not only the sidebands of inductor current loop needs to be considered
but also the sidebands of capacitor voltage loop
Up to now, there is no equivalent circuit model taking capacitor voltage sideband into consideration
From the describing function result
The capacitor voltage feedback cause a pair of double pole at half of switching frequency
From the bode plot, the gain is one at low frequency
which means that the output voltage can well follow the control signal at low frequency
At half of switching frequency there is a peaking
Physically it means that the capacitor voltage feedback turns the circuit into a non-ideal voltage source
Our proposed equivalent circuit model is based on the previous non-ideal voltage source concept
From our knowledge of current mode control
the inductor current is well controlled by control signal Vc2
For V2 control, Vc2 signal is composed by Vc1, Vcap(fm), and sideband frequency Vcap (fsw-fm)
This is our proposed equivalent circuit model
Vc1(fm), is responsible for the red current source
Vcap(fm) is represented by a resistor RCo
By thevenin's theorem, we can see that this resistor basicly turns the current source into a voltage source
The effect of sideband frequency of Vcap, Vcap(fsw-fm)
is represented by an inductor Le2 in series with a resistor Re2
Which represents the non-ideal voltage source as Le2 and Re2 will form the double pole at half of switching frequency by resonance with output capacitor
Le2 determines the double pole position and Re2 is related with the damping of this double pole.
Therefore, this simple equivalent circuit shows that capacitor voltage feedback turns the current source into the non-ideal voltage source
Now for a general case, the inductor current sideband information also needs to be considered
This graph shows the equivalent circuit
The equivalent circuit model reveals that the inductor current feedback turns the power stage into a non-ideal current source
The non-idealness of this current source is shown in equivalent circuit by resonance between Ce and Ls
The capacitor voltage feedback turns current source into a non-ideal voltage source
The non-idealness of this voltage source is by resonance between Le2 and output capacitor Co
Now by considerring the input property the same way as in unified current mode control
we can get the complete equivalent circuit model, and this model can be used to derive all transfer functions
This shows simulation verification for OSCON capacitors
Control-to-output, Audio susceptibility, output impedance and input impedance are compared
We can see that the proposed equivalent circuit model agrees with simulation results very well up to half of fsw for all four transfer functions
This shows simulation verification for two-phase constant on-time V2 control with Ceramic capacitors
Again, the proposed model can predict the double pole very accurately and it agrees with simulation results very well for all four transfer functions
This shows simulation verification of control to output voltage transfer function for constant frequency V2 control
For both cases using OSCON Caps and ceramic caps, control to output voltage transfer function can be designed
as a flat gain up to very high frequency and the model agrees well with simulation result up to 1/2 fsw
This is the experimental waveform based on LM34930 demo board
with traditional 10uF ceramic caps, which has small ESR around 5m, we can observe there is an instability problem
which is predicted from our model as the system has a right half-plane double pole
Now use the customized ESR caps which has 50m ESR, we can see now the circuit is stable
which is predicted from our model as the system has a left half-plane double pole
Now we do measurement of control-to-output transfer function to verify our model
the measurement is based on network analyzer Agilent 4395A. This shows the measured transfer function
We can export the data and compare with the equivalent circuit model
we can see the prediction from equivalent circuit model can match well with experimental date up to half of fsw
That is all for this vedio
if you have any questions or comments, please feel free to discuss with me, thank you