Cursed circuits: charge pump voltage halver

lcamtuf’s thingSubscribeSign inCursed circuits: charge pump voltage halverThere's plenty of circuits that are hard to understand because they're complicated. And some that are hard to make sense of because they seem too simple.Dec 02, 2025142ShareIn the spring of 2023, when this Substack had only a handful of subscribers, I posted a primer on voltage adjustment in electronic circuits. The article opened with a brief discussion of linear regulators, and then promptly threw them under the bus in favor of more efficient charge pumps and inductor-based topologies.The basic charge pump architecture — a voltage doubler — is quite elegant and easy to understand. It’s also far more common than many people suspect: the circuit can be constructed directly on a silicon die, so it shows up inside quite a few digital chips, from modern op-amps to MCUs. If you weren’t a subscriber back in 2023, or if you don’t have a photographic memory for random blog articles, a conceptual diagram of the pump is shown below:The operation of a rudimentary charge pump.In the panel on the left, we see a Cout capacitor that’s perched on top of the positive rail while a “flying” capacitance Cf is charging from the power supply. The charging process produces a voltage that’s internal to the component: we can unplug Cf, put it in our pocket, and then hook it up to another circuit to power it for a brief while.In the second panel (right), we see the second part of the cycle: Cf is disconnected from the supply and then hooked up to the terminals of Cout. This action transfers some of the charge from Cf to Cout, up until the voltages across the terminals of the capacitors are equalized. After several of these roundtrips, VAB should approach Vsupply. Of course, VBC is also equal to Vsupply; it follows that the voltage between A and C must be the sum of the two, or 2 · Vsupply.In other words, the circuit is a voltage doubler; the repeated motion of Cf ensures that the charge in Cout is continually replenished if we connect any load between the points A and C. There will be a bit of voltage ripple, but the amount can be controlled by sizing the capacitors and choosing the operating frequency to match the intended load.Naturally, practical charge pumps don’t mechanically move a capacitor around. Instead, they use transistors configured as switches to alternately connect Cf to to the supply and to the output cap, an architecture that can be sketched the following way:A more practical outline of a charge pump voltage doubler.The transistors themselves can be driven by a simple relaxation oscillator or by a programmable digital chip.A similar circuit can be used to produce negative voltages: we do this simply by dangling Cout from the negative supply rail instead of perching it on top of the positive one. This modification effectively places the capacitor’s bottom terminal at -Vsupply.So far, so good. But this brings us to a more perplexing flavor of the charge pump — the voltage-halving topology shown below:A mildly cursed “voltage halver”.What’s that, you might ask — a capacitor-based voltage divider? Well, yes and no. Capacitors can be used as voltage dividers for AC signals: they exhibit a resistance-like effect known as reactance, so if you have an alternating sinusoidal waveform, you can attenuate it that way. That said, the divider doesn’t really work for DC voltages, because at 0 Hz, the reactance approaches infinity.To grasp the design, ignore Cf and the attached load. Let’s focus just on the pair of series capacitors: C1 and C2. When these two capacitors are first connected to the power supply, they can be analyzed as a single composite capacitance, with some common charging current that will briefly flow through this circuit branch. In particular, if C1 = C2, the common current will produce roughly the same charge state for each capacitor, resulting in VAB ≈ VBC ≈ Vsupply / 2.This sounds like the outcome we’re after, but once the common charging current ceases, there’s nothing to keep the voltages the same. In particular, if we connect a resistive load across terminals B and C, the bottom capacitor will discharge to 0 V; the reduction in the voltage at point B will also allow the upper capacitor to charge in a way that makes up the difference. A momentary current will flow, but the end state is VAB = Vsupply, VBC = 0 V, and Iout = 0 A.This sounds useless, but that’s where the flying capacitor — Cf — comes into play. If it’s moved back and forth between C1 and C2, it will charge from the capacitor that sits at a higher voltage and then discharge into the one that’s at a lower voltage; in our example, it will continually replenish the charge in C2, allowing a steady current to flow through the load.The stable equilibrium for this charge transfer process is reached when VAB ≈ VBC ≈ Vsupply / 2 — so in contrast to conventional voltage dividers, the output voltage is always at the midpoint between the supply rails, with no dependency on the relative values of C1 and C2. Pretty neat!Subscribe142ShareDiscussion about this postCommentsRestackslcamtuf 6hEditedPinnedRelatedly: it's also possible to build a switched-capacitor lowpass filter. An input capacitor connected to the source and charges to a voltage equal to the current input signal; it's then disconnected from the source and connected to a second capacitor, to which it transfers some of the charge. The ratio of the two capacitances, along with the switching frequency, determine how quickly the voltage in the second capacitor can increase or decrease -- a lowpass effect.This is noisier than R-C filters, but is easier to make on an IC die, so such filters are sometimes found in certain signal-processing chips.Expand full commentReplyShare1 reply1 more comment...TopLatestDiscussionsNo postsReady for more?Subscribe© 2025 lcamtufPublisher PrivacySubstackPrivacy ∙ Terms ∙ Collection notice Start your SubstackGet the appSubstack is the home for great culture

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The article, penned by lcamtuf, delves into the intricacies of charge pump circuits, specifically examining their voltage halving topology. The piece begins by establishing the prevalence of charge pumps in modern digital circuits, highlighting their use within op-amps and microcontrollers due to their efficient voltage doubling capabilities. The core operation of a basic charge pump – employing a flying capacitance (Cf) – is explained, detailing how Cf repeatedly charges and discharges, effectively transferring charge between capacitors Cout and C1/C2, ultimately approaching a stable output voltage of Vsupply/2.

However, the author then introduces a more perplexing design: a voltage-halving topology utilizing only C1 and C2, without the flying Cf. This arrangement, initially appearing counterintuitive, exhibits a behavior that becomes fully explained with the inclusion of the flying capacitor. The circuit is analyzed as a series capacitor configuration, where C1 and C2 are initially connected to the power supply, establishing a common charging current and approximately Vsupply/2 across both capacitors. The analysis focuses on the transient behavior of this system, noting that once the charging current ceases, a resistive load connected across terminals B and C results in a discharge of the bottom capacitor and a charging of the top capacitor, ultimately leading to VAB = Vsupply and VBC = 0V.

The key to understanding this seemingly problematic circuit is the revival of the flying capacitor (Cf). Inserting Cf into the system allows it to continuously shuttle charge between C1 and C2, maintaining a constant flow through the load. This continuous charge transfer ensures that the output voltage always remains at Vsupply/2, independent of the values of C1 and C2. The author notes that this configuration doesn't behave like a standard voltage divider because the flying capacitor is continually intervening to maintain charge balance.

Furthermore, the article extends the discussion by mentioning a related application: switched-capacitor lowpass filters. It describes how the fundamental principles of charge pumps – including the charging and discharging of capacitors and the tuning of switching frequencies – can be applied to create filters. The author emphasizes the noise characteristics of switched-capacitor filters compared to R-C filters, acknowledging their relative simplicity for integration onto an IC die.

The lcamtuf piece effectively dissects a deceptively simple circuit, revealing the underlying principles of charge pump operation and showcasing their versatility in different applications, including voltage halving and filter design. It highlights the strategic importance of the flying capacitance in maintaining stable voltage levels, as well as acknowledging the associated trade-offs, such as the increased noise associated with switched-capacitor filters. The writing clearly articulates the theoretical underpinnings, making accessible the somewhat unconventional behavior of this charge pump configuration.