Charge pump needs many iterations?

Hello,

I read the following from Wikipedia:


According to Wikipedia article:

To describe the ideal operation of the circuit, number the diodes D₁, D₂ etc. from left to right and the capacitors C₁, C₂ etc. When the clock Φ1 is low, D₁ will charge C₁ to Vin. When Φ1 goes high the top plate of C₁ is pushed up to 2Vin. D₁ is then turned off and D₂ turned on and C₂ begins to charge to 2Vin. On the next clock cycle Φ1 again goes low and now Φ2 goes high pushing the top plate of C₂ to 3Vin. D₂ switches off and D3 switches on, charging C3 to 3Vin and so on with charge passing up the chain, hence the name charge pump. The final diode-capacitor cell in the cascade is connected to ground rather than a clock phase and hence is not a multiplier; it is a peak detector which merely provides smoothing.[2]

A critical question is that when C₁, with Q=C1Vin, is raised to 2Vin by Φ1, when charging C₂ it will lose charge and the voltage will drop. The same problem extends to all subsequent chaining steps.

After carefully thinking I still feel it a legit question and don’t see why it is left unexplained. I actually suspect the charging process takes multiple iterations to reach equilibrium: in each iteration the charging capacitor (like C₁) gives some charge to the next one (C₂), and regains the lost capacity in the next iteration. Several iteration are needed to final charge output (Vo) to the desired value, but NOT in one iteration.

Could anyone explain this problem?


Matt

Well, of course you need multiple charge impulses to
fill the larger reservoir. And yes, there is always some
"back-flow" which you must tolerate and/or design
against; in low voltage designs especially, this is the
largest challenge (your box between reverse leakage
and forward current, between (Vdd-Vf*N) and Vr,
Cflycap vs Cdiode). There are plural losses, balancing
them and minimizing them is the designer's job.

Hi dick_freebird,

Could you refer to some more detailed material explaining the multiple charge process?

I actually looked at two books about charge pump design:

1. Charge pump circuit design by Pan & Samaddar
2. Demystifying Switched-Capacitor Circuits

However when discuss Dickson charge pump, both books seem to assume that the charging was like some "one-shot" process, just as the Wikipedia explanation did.

Do we have some more detailed analysis?


Matt

Each of the capacitors will only transfer charge up to Vin*C each cycle, but as you go further down the chain capacitors will require more charge than that to reach their steady state voltage. So there's obviously no way the circuit can go from no charge to steady state in just one cycle. If you wanted you could derive the charge transfer per cycle and find the transient response.

I think the description from wikipedia assumes that all of the capacitors are charged to near their steady state voltages.