Whatever your applications design(s) — digital multimeter, oscilloscope, on-board charger (OBC), plug-in battery for hybrid or electric vehicles, power supply for a motor drives, etc. — it needs to include overcurrent protection. To that end, you might want to introduce a component that protects your circuit when the smoothing capacitor C of the SMPS in Figure 1 pumps a very high current at the device’s initial switch on, or when a faulty voltage input is applied for a long time at the ohmic measurement input of the multimeter in Figure 2. In this last circuit, the Zener diode will clamp a too high input voltage, but the current produced could be damaging if applied for a too long time.

PTC ceramic disc components are universally used for overcurrent circuit protection. The principle of their function is relatively simple. Let’s look at the electrical resistance characteristic as a function of temperature (Figure 3).

At a low temperature (low voltage), the component’s electrical resistance R is low, and in the case of a current surge or external temperature increase, the component heats up. The electrical resistance value increases drastically once the component reaches a temperature known as the switch temperature (Ts). Ts is defined by the material used to manufacture the component and can be adjusted at will by a proper mix of oxides Ba(Sr,Pb)TiO3.

Thus, at a low ambient temperature the PTC lets the normal current flow into the circuit, and above the Ts point it acts as an open circuit. However, in practice the phenomena underlying a PTC’s behavior are extremely complex and the equations describing them are seldom decipherable.

If you need to use a PTC in your application, there are two classic ways to explore. The first is the highly scientific way. For example, you might read articles about the Heywang model [1] and immerse yourself in the interesting principles of the grain boundary’s resistivity changes, coupled with the Curie temperature effect.

If you don’t have the time to dedicate to studying, the second approach is to go directly to a component’s datasheets. Be sure to look at Vishay’s document “PTC Explanation of Terms” [2], which describes the numerous PTC parameters, from *T _{s}* to the voltage-dependent resistance (VDR) effect and trip and non-trip currents. All these characteristics will have to be taken into account for a high performance and reliable design.

These two classic approaches are intellectually enriching and they will challenge your engineering skills. Be sure that you have enough time though, because designing-in a PTC that works properly in the application is a tricky job (we haven't talked about analyzing the influence of all the aforementioned parameters’ tolerances, and of course about wide potential variations of the ambient temperature).

So, one might wonder if there’s another method allowing for direct trial and error, a kind of plug-and-play approach that’s free, if that’s not too much to ask.

**Enter LTspice**

This might sound like a song’s chorus, but really, it’s worth repeating: in order to produce useful results with simulators like LTspice, you will first need good PTC models. And good models must in fact give a faithful image of the specifications. If modelling is done with this in mind, then the user will be able to combine all the modeled specification points at the same time in one simulation, showing all the interactions between them. And I’m speaking about the voltage-dependent effect, the thermal mass, dissipation factor, ambient temperature effect, resistance variation as function of the temperature, trip and non-trip current — all the tolerances on all of these can be tested at the same time. There will be no need for complex explanations anymore. Simply select a component according to a common-sense guess and you can visualize the complex conduction phenomena during the simulations.

After researching popular simulation software, some PTC models from outdated part numbers were found. These were unfortunately useless. The time was thus ripe to update overvoltage PTC modeling and for practical reasons we chose a widely available simulation software: LTspice from ANALOG DEVICES. It was applied to the PTCTL (overcurrent protection), PTCCL (current limiter), and PTCEL (surge arrester) from Vishay.

For the results, let’s look at the simulation in Figure 4. This small circuit illustrates the case of a PTC switching when an AC overvoltage of 800 V at 50 Hz is applied to a Vishay PTCCL05H100SBE (*R*_{25} = 1600 Ω) in series with a load having a resistance of 1000 Ω. The simulation is repeated at three ambient temperatures. The current decreases in time as the PTC heats up, showing a shorter switching time when the ambient temperature increases (Figure 5). Look at the flattening of the current form when it approaches 0; this is the VDR effect. At low voltage, the apparent resistance of the PTC is higher.

A second simulation

A second simulation (Figure 6) shows the function of the PTC as a resettable fuse. A voltage variable in time V(mains) is applied to another Vishay PTCEL (surge arrester). The three panes of Figure 7 show that as soon as the current into the PTC goes above a defined value (non-trip current of 120 mA), the PTC heats up and switches to high resistance values within a time period dependent on its electrical resistance tolerance (Monte Carlo analysis). After 1300 s (arbitrary time), when the voltage comes back to 220 V, the PTC remains switched at a high resistance (middle pane) and the mains voltage needs to be tuned down to a low value (t = 1800 s) to allow the PTC to cool down and to return to its low initial resistance.

Now we get back to the applications mentioned at the beginning of this article: let's more closely examine a ceramic PTC as an inrush current limiting device for OBCs, plug-in batteries for hybrid or electric vehicles, as well as power supplies for motor drives.

In the example in Figure 8, the secondary winding of a three-phase transformer (ph1 to ph3) provides power to a load after voltage rectifying and smoothing by a DC-Link capacitor C1. For the purpose of this simulation, the load (normally connected in parallel to C1) is not represented.

The design problem is in defining how many PTCs you need to place in parallel (two in Figure 8) in order to ensure that no PTC switches in normal conditions. In the case of a PTC switch, the voltage of capacitor C1 will never reach a value near the maximal swing of the AC source. Figure 9 shows the simulation of the voltage on C1 charging for three ambient temperatures (0 ^{o}C, 25 ^{o}C, and 50 ^{o}C) with two (red curve), three (yellow curve), or four (white curves) PTCs in parallel. We see that there are problems with only two PTCs reaching the maximal voltage, especially when TEMP increases. Using three or even four will put the application on the safe side.

Using an electronic simulation allows for the hands-on testing of more combinations of PTCs in series and in parallel (as some suppliers recommend [3]). Figure 10 presents an example of a circuit with only one PTC (left side) in comparison with the same circuit with four PTCs (a network of two parallel branches of two PTCs in series) having the same average resistance but an enhanced thermal capacity. Figure 11 presents the simulation results of a circuit with one PTC (higher pane) and four PTCs (lower pane). We effectively see that the PTC network allows for the capacitor to charge at the top of the voltage swing while the single PTC tends to switch before this capacitor is charged.

Of course, because of the restricted number of PTC SPICE models available on the market at this moment, it’s not guaranteed that you’ll find the right component that meets all your expectations. In that case, don't worry, the good old methods will always be applicable.

The generalization of SPICE PTC modeling has only just begun, and of course, Rome wasn’t built in a day, as the saying goes. It’s remarkable though that after more than 30 years of SPICE [R]evolution, one can still find component types without readily available accurate models. The PTC SPICE models presented in this article can be downloaded here.

The presented simulations or specific requests for PTC SPICE models can be obtained by emailing here.

**References**

- Theoretical Aspects of PTC Thermistors, Sang-Hee Cho, Journal of the Korean Ceramic Society, Vol. 43, No. 11, pp. 673-679, 2006.
- PTC Explanation of Terms, 2018, web
- PTC thermistors for overcurrent protection and as inrush current limiters, TDK, 2018, web

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