Decades after invention of the Cockcroft-Walton voltage multiplier, it is still being used in broad range of high voltage and ac to dc applications. High voltage ratio, low voltage stress on components, compactness, and high efficiency are its main features. Due to the problems of original circuit, reduction of output ripple and increase of accessible voltage level were the motivations for scientist to propose new topologies. In this article a comparative study on these voltage multipliers was presented. By simulations and experimental prototypes, characteristics of the topologies have been compared. In addition to the performances, components count, voltage stress on the components, and the difficulty and cost of construction are other factors which have been considered in this comparison. An easy to use table which summarized the characteristics of VMs was developed, which can be used as a decision mean for selecting of a topology based on the requirements. It is shown that, due to the application, sometimes a simple and not very famous topology is more effective than a famous one.

High voltage dc power supplies are widely used for many applications, such as particle accelerators, X-ray systems, electron microscopes, photon multipliers, electrostatic systems, lasers systems, and electrostatic coating [

Historically the original idea was proposed by Greinacher in 1921. However, it did not get attention for a long time until Cockcroft and Walton performed their experiment using this circuit in 1932 [

The comparison of these VMs is important because selecting a topology for an application due to many factors involved is not a straightforward task. The range of output voltage level, necessary safety factors, ground-returned or bipolar output, and speed of response and so on are the main factors which should be considered in such selection. To the best of author’s knowledge, until now such comparison has not been made.

This paper is organized as follows. The mathematical model of the CWVM is reviewed in Section

Figure

Schematic circuit of a basic 4-stage Cockcroft-Walton voltage multiplier.

However, this is not the case in presence of a load, which output voltage ripple exists and there is a drop in voltage due to the load current. To be clear, in Figure

Simulation of a conventional 4-stage

Because ripples on all smoothening capacitors are in-phase, the total voltage ripple on load can be calculated by summation of all ripples values; that is,

Recently with more detailed analysis it has been shown that the above formula needs a small correction [

To exceed the restriction of (

As mentioned in previous section, by increasing number of stages, the ripple amplitude and drop voltage increase significantly, which make the voltage multiplier inefficient. To solve this problem a symmetrical voltage multiplier (SVM) was developed by Heilpern in 1954 by appending an additional oscillating column of capacitors and a stack of rectifiers [

Schematic diagram of a 4-stage SVM.

Output voltage ripple of a symmetrical voltage multiplier for two cases of in-phase and 180° out of phase power sources.

It is shown that the ripple in symmetrical case compared to the original VM can be reduced approximately by the following formula [

In practice, any kind of asymmetry may result in higher value of ripple. It is known that the asymmetry of both input voltages and circuit elements can cause the ripple [

Recently a new symmetrical voltage multiplier has been proposed [

Schematic diagram of a 4-stage HSVM.

As mentioned earlier the main features of a symmetrical voltage multiplier are lower voltage ripple and higher voltage level due to the complementary action of each half section of the multiplier. It means each half section compensates ripple of the other half due to 180° phase differences between the resulting voltage ripples. It is possible to have such condition with two series-connected voltage multipliers. In Figure

Schematic diagram of a series-connected voltage multiplier (SCVM).

Based on this idea, it is possible to build a three-phase (or even higher) VM with cascading three (or more) VMs whose power sources have 120° (360°/number of phases) phase differences with each other. The ripple of such 3-phase VM will be lower than that of two-phase symmetrical VMs. However three separate transformers and several times of components are needed, which make the circuit more costly and bulky [

When we cascade two conventional voltage multipliers with 180° out of phase voltage sources as Figure

Schematic diagram of a series-connected positive-negative voltage multiplier.

In Figure

In this section, by Saber Synopsys software, simulation results of previously discussed VMs are compared. Input voltage and number of stages are chosen to get almost equal output voltage from all VMs. Therefore by consideration of devices count and output specifications of voltage multipliers, comparison is done. Nonideality of the components that are considered in simulations is ESR of capacitors

The structure of transformers of VMs is a matter which should be discussed in more detail. Some of the VMs use transformers with two secondary windings, such as SCVM and SVM. If we want to use the same transformer for all VMs, to have the same condition for comparison, a transformer with two secondary windings should be used. Then, in topologies that use one voltage source, series connection of secondary windings could be used. Therefore, for those topologies which need one secondary winding, the voltage would be twice of those with two secondary windings. However, in this case, the stress on components in SVM and SCVM is equal to half of that for other topologies and the number of stages should be doubled to have similar value of output voltage. HSVM also has the same condition and therefore, to decrease the number of stages, a transformer whose secondary voltage is twice of those for BVM and SPNVM could be used. It means there are two choices: first to use the same transformer for all VMs and second to consider the same stress on components. In simulations it is found that SCVM response is almost similar to that of SVM. Furthermore its transformer has the mentioned problem of extra voltage imposed between windings. So in simulations and experiments the SCVM was omitted.

In simulations and experiments, based on abovementioned matter about transformer, two versions of HSVM and SVM are considered. HSVM1 is an eight-stage VM with 10 V input. HSVM2 is a four-stage VM with 20 V input. SVM1 is an eight-stage VM with two 5 V inputs. And SVM2 is a four-stage VM with two 10 V inputs. SPNVM and BVM are four stages with 10 V input. It must be emphasized that the voltage stress on components in topologies depends on the transformer voltage. That is, the magnitude of voltage stress on HSVM1 and SVM1 components is half of that for others. So in components count we should consider this matter. We know that a capacitor with _{1} is twice of that for VM_{2}, in components count we can consider capacitors and diodes of VM_{2} as basic components and multiply the number of capacitors of VM_{1} by four and its diodes by two, to find out equivalent number of similar components. With this method we can correctly compare the number of components, that is, the cost of construction. This matter is considered in comparison between VMs. The discussed matter of this paragraph should be understood carefully to know why the proposed comparison in this article is fair.

The frequency of voltage sources (transformers output) is 2 KHz and capacitors in all VMs are 1.6

Simulation results: transient and maximum values of output voltages of VMs.

Figure

Simulation results: output ripples of voltage multipliers at steady state.

To verify the simulation results, prototypes of VMs have been constructed. BVM, SPNVM, HSVM1, HSVM2, SVM1, and SVM2 have been constructed for comparison. Input is a 2 kHz sinusoidal source with variable amplitude which combined with a ferrite core transformer provides the requested voltages. As in simulation a purely resistive 51 kΩ load is used. Capacitors are in range of 1.62

In Figure

Experimental results: transient responses of VMs. SPNVM with 14.39 ms rise time has the fastest response and HSVM2 with 70.4 V has the maximum output value compared to others.

In Figure

Experimental results: peak-to-peak value of ripple of VMs. SPNVM with 456 mV ripple has the smoothest response compared to others.

In Table

Summary of VMs specifications.

Voltage Multiplier | BVM | HSVM1 | HSVM2 | SPNVM | SVM1 | SVM2 | |
---|---|---|---|---|---|---|---|

Number of capacitors | 8 | 22 | 10 | 8 | 24 | 12 | |

Number of diodes | 8 | 32 | 16 | 8 | 32 | 16 | |

Number of secondary windings | one | one | one | one | Two | Two | |

Transformer windings voltage (V): | 10 | 10 | 20 | 10 | 5 | 10 | |

Secondary wire factor | 1 | 1 | 2 | 1 | 1 | 2 | |

Voltage stress on components (V) | 20 | 10 | 20 | 20 | 10 | 20 | |

Base-cap number | 32 | 22 | 40 | 32 | 24 | 48 | |

Base-diode number | 16 | 32 | 32 | 16 | 32 | 32 | |

| |||||||

Simulation results | |||||||

| | 58.7 | 50.35 | | 69.63 | 44.59 | 68.81 |

Ripple (V) | 3.11 | 0.563 | 0.513 | 0.496 | 0.477 | 0.484 | |

Ripple factor | 0.052 | 0.011 | | | 0.010 | | |

Rise time (ms) | 19.6 | 20.6 | 13.9 | | 24.8 | 16.2 | |

| |||||||

Experimental results | |||||||

| | 57.6 | 50.4 | | 68.0 | 44.0 | 68.0 |

Ripple (V) | 3.04 | 0.648 | 0.500 | 0.456 | 0.560 | 0.480 | |

Ripple factor | 0.052 | 0.012 | 0.007 | | 0.012 | 0.007 | |

Rise time (ms) | 22.7 | 21.1 | 18.45 | | 27.32 | 20.23 |

Decades after invention of Cockcroft-Walton voltage multiplier, in broad range of high voltage and ac to dc conversion applications, it is still being used and has no competitor. In this paper a review over and a comparison between symmetrical versions of VMs were carried out. The features of different VMs as rise time, ripple, and output voltage are compared to each other with regard to the complexity of the topologies and number of components. In this comparison, some factors as voltage stress on components, number of components, and transformer construction cost are considered. In fact, the voltage stress on components can be used as a factor to evaluate the effective number of components and consequently the price of VMs.

Ground problem of transformer in some VMs makes them ineffective especially in very high voltage usage. However, in mobile apparatus and some low voltage applications, they still can be used. For example, SPNVM with low components count and acceptable characteristics is an attractive choice which should not be ignored in such applications. With simulations and experimental prototypes, the responses of VMs were compared. The measured values of the prototype’s waveforms agreed well with their counterparts simulations. In summary it is not possible to choose one topology as a perfect one. In fact, in each application based on the level of output voltage and therefore components price, with similar method used in Table

The author declares that there is no conflict of interests regarding the publication of this paper.

The author would like to thank his colleagues Mr. M. Daneshyan and Mr. B. N. Mortazawi for their help in preparing experimental tests. This work was supported by project from “Laser & Optics Research School” (Code no. PRD-L2-93-007).