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Discover The Secretes Of Printed Heater Design Now - A Design Guidebook

Author: Dr. H David Rosenfeld, h.rosenfeld@celanese.com

Electrical resistance heaters

Electrical resistance heaters can take many forms. They might be wires, ceramics, textiles, films, printed conductive inks and pastes, or some other form. Regardless of form, they all work on the principle of Joule Heating, where a flow of current through a resistance creates heat. The rate of heat production (power) is proportional to the square to the current. The coefficient of proportionality is the resistance of the conductive element,

Ohm's law, V=IR, relates current to voltage allowing this to be written

This last form is most useful, since voltage is typically specified, and the resistance is selected to fix both the current and the power to desired levels.

All electrical resistance heaters are 100% efficient in converting electrical energy into heat. Electrical power in equals heating power out. However, the physical form of the heating element can have a big impact on how that heat flows away from the heating element towards the surface that is to be heated. Film heaters, made by printing functional inks/pastes onto a flexible substrate can be very effective in delivering heat to the surface of a seat, a panel, or the wearer of a heated garment. Unlike metal wire heaters, the power is produced over a large area. The thermal gradient it produces is effectively unidirectional and heat flows directly toward the desired surface. Printed film heaters are thin and smooth. They don’t need to be padded to prevent them from printing through or causing user discomfort. This means faster warm-up and less energy wasted heating the thermal mass of the padding. For these reasons, printed film heaters can deliver the same thermal performance on the surface of interest with less energy input. In this way, they can be said to be more efficient in converting input power to surface heating.

Printed PCB carbon film heater

Functional pastes for printing film heaters can be either fixed resistance or so-called positive temperature coefficient (PTC) pastes. The later having the property of increasing resistance with increasing temperature. Since heating power is proportional to resistance, this means they produce less power as they get hot. They are sometimes referred to as self-regulating. Micromax™ has several PTC pastes to select from with different resistance responses to temperature. An example is PTC085, which rapidly increases resistance as its temperature approaches 85C. More on this later. Fixed resistance pastes can be used to print two styles of heater circuit. A highly conductive paste can be printed in a serpentine pattern to mimic the design of a wire heater. We call this style a printed wire. Printed wire heaters are usually made with silver conductive pastes. The high conductivity is needed to allow for a long trace with sufficiently low resistance. An example is shown in figure 1.

Figure 1. Photo of printed wire heater (butterfly heater). Silver with carbon overprint.

Both PTC and non-PTC pastes can be used to form tile heaters. These are created by running two parallel busses of a high-conductivity paste with inter-digitated fingers extending between them. One bus is positive, and the other is negative. Tiles of a less conductive paste are then applied to connect opposing fingers (Fig. 2). The tiles are the heating elements and are usually formed with a carbon-based paste, either fixed resistance or PTC. It is best if the tiles are kept small, on the order of a centimetre or less in any dimension, in order to avoid hotspots caused by the uneven thickness of the print. This usually requires the paste to have a high sheet resistance as printed. A few hundred Ω/□ (ohms/square) or more. PTC carbon pastes fit this requirement very well.

Figure 2. Tile heater (seat heater design)

Both tile heaters and printed wire heaters find practical applications. A printed wire design is simpler to produce. It might be done in a single print layer. If PTC is desired, a tile heater design must be used, since the resistance of the PTC pastes will almost certainly preclude any wire-type design with it. In some cases, the heating elements might need to extend a long distance from the connection to the power supply. This often makes a printed wire heater impractical, since a very wide element would be needed to keep the resistance of the total circuit low enough to produce the power needed. While it may seem counterintuitive, a carbon tile heater might use more silver than a printed wire of the same size and power. Depending on current levels, a tile heater might need a very wide bus to limit parasitic heating losses. The bus and all the silver fingers add up. It can sometimes be very challenging to print a uniform thickness in a printed wire design where the print changes direction, especially if the elements are wide. A tile heater can provide very uniform heating over a large area. It is even possible to adjust tile size to provide different levels of heating in different areas, or to correct for power losses in the bus. With these thoughts in mind, let’s move on to establishing operating parameters and material selection.

High Voltage Coolant Heater

Operating Parameters and Materials Selection

From an electrical perspective we need to know at least two of the following four parameters:

power (watts)
voltage (volts)
current (amps)
resistance (ohms)

From any two, one can calculate the remaining values from Ohm’s law, V=IR, and the power relationship P=IV. If the printed film heater is replacing an existing not-in-kind heater, we can start design using the same power, voltage, etc. and then evaluate performance of the printed film heater to see if an adjustment in resistance is required.

Operating temperature needs to be considered. Even if the electrical parameters are specified, we need to make sure our material set is suited to the temperatures it will experience in use. For heater element temperatures at or below 100C a polymer thick film (PTF) paste may be appropriate. An Intexar™ paste on TE-11C thermoplastic polyurethane substrate, or another Micromax™ PTF paste on flexible polyester could be the right choice. Micromax™ PTC carbon pastes are suited to this temperature range. For higher temperatures up to 300C a polyimide substrate functionalized with Micromax™ HT series pastes would be required. For still higher temperatures, a fired-on solution on a ceramic or metal substrate would be needed. The Heatel™ series of products allows heater circuits to be printed on stainless steel. Aluminum can be used with our lower firing temperature AS series. Products are also available to print heating circuits onto a variety of ceramics – alumina, BeO, AlN, etc.

Temperature is also considered in a new application where there is no existing heater from which to extract power requirements. It is common to see requests for a heater of a certain size that will heat to a certain temperature. How can the operating temperature be related back to the power requirements? When power is applied to a heater it will begin to raise the temperature above the ambient temperature. The amount of temperature increase above ambient will be proportional to the power of the heater divided by its heated area,

The coefficient β will depend on how heat flows in and out of the object being heated. The power per unit area is referred to as watt density and is usually given in watts per square inch (wpsi) or miliwatts per square cm. How much watt density is needed must be determined through thermal modelling, or by experiment.

As Joule Heating occurs, the temperature of the heating element will rise. Heat will flow from it to the objects around it. Mostly by conduction, but some will also be lost to convection as air circulates around the object. At very high temperatures radiative losses may also become significant. The temperature of the heater and the objects around it will rise until the heat flowing out and away is equal to the power input to the heater. This is thermal equilibrium. The temperature at which it occurs will depend on how heat flows and the temperature of the surrounding environment. In many applications the ambient temperature, and even how heat flows, are subject to change. Controlling to a specific temperature requires thermostatic control to regulate power to the heater, usually by controlling duty cycle, turning it on and off as required. PTC materials improve the situation by becoming more resistive as temperature increases. This reduces power input, and with it the equilibrium temperature. This can help to compensate for changes in the environment and leads to a self-regulating system. Each application should be evaluated to determine if the degree of self-regulation provided by the PTC material is sufficient for safe operation, and if any applicable regulations require use of active temperature measurement and control.

Heated jacket

One other factor needs to be considered when deciding on heater power. How fast must it warm up? Since power is the rate at which the heating energy is being supplied, faster warm-up needs more power. This is where PTC can provide additional benefit. It will have a lower resistance when cold, providing more power for warm-up, then as the system warms, resistance increases to limit steady state operating temperature. Achieving something similar with fixed resistance is possible by duty cycling a more powerful heater once operating temperature is reached, requiring thermostat control. In some applications where the power supply is very limited, care must be taken to avoid excessive current draw at cold start. Garment heaters operating on 5V, 2A USB battery packs are an example where this can be a problem. PE672 carbon paste was developed to address this. It has very little resistance increase with temperature. The table below shows the time required to heat a 1mm thick stainless-steel plate 50C above ambient for various watt densities.

For reference, most heating pads, electric blankets and pet warmers are in the range of 0.2-0.3W/in2 (30-50mW/cm2). Any design for contact with people and pets should be thoroughly reviewed to ensure safe skin contact temperature in operation.

Once the power requirement is known, we can consider the power supply. This will determine limits on voltage and current available to power the heater. It could be an automotive system at 13.5V with an alternator that can deliver large amounts of current if needed. It could be a low power supply like the aforementioned USB battery back, limited to 5V and 2A. Or it could be household mains AC. If a choice in operating voltages is available, it is generally best to aim high. A high voltage allows for lower current operation to produce the same power. This means overall circuit resistance can be higher allowing thinner, longer design elements, or reduced paste laydown. It also means lower parasitic losses due to the resistance of the bus and leads. Electric vehicles often have very high voltages available. Micromax™ pastes, including PTC pastes, have been tested at voltages as high as 1500V, with voltage gradients as high as 250V/mm.

Once power and voltage have been determined, current and resistance are fixed as well. We are now armed with enough information to proceed to design the heater circuit itself.

Flexible Heater

Heater Component Geometries

Both tile and printed wire heaters are designed with the concept of resistive units called squares. The resistance of a printed conductive paste will depend on the geometry of the print. If one prints thicker, resistance goes down. If the print is made longer, resistance end-to-end goes up. A wider print will have less resistance. The resistance is related to the geometry through the volume resistivity, ρ.

The ratio l/w is referred to as the number of squares in the geometry. For a given print thickness the resistance will be constant, when the ratio of length to width is fixed. A 100mm long, 1mm wide trace would be 100 square, as would a 50mm long, 0.5mm wide trace. The mks units of volume resistivity are Ohm-m. It is sometimes given in units of ohms/square/mil (Ω/□/mil). It is very helpful to know how thick a paste typically prints in a single print pass. With the volume resistivity given in Ω/□/mil, one can simply divide by the print thickness (in mils), or if the thickness is in microns, multiply by 25.4 then divide by thickness. This yields the sheet resistivity in ohms per square, ρs. Armed with this value, we can now calculate the resistance of any geometrical element of our heater based on the length along the direction of current flow and the perpendicular direction width.

From here, design of a printed wire heater is straightforward. Knowing the required total resistance from the previous discussion about heater power density, the resistivity of the selected paste and how thick it will print, we can calculate the number of squares via

This yields the ratio of length to width for the printed heating element.

Example: Printed Wire Heater

A 10cm x 10cm area is to be heated with a watt density of 50mW/cm2 using a printed wire design and 13.5V power supply with current up to 5A.

Through the relations we developed previously (equation 2), R = V2/P, so here we want R = 13.5V * 13.5V / 5W = 36.5Ω. Now a decision must be made about what paste to use. There are a number of ways to approach the decision. The choice can be based on desired geometry for uniform coverage of the heated area, or a conductive paste can be selected, and geometry set to accommodate it. Often a hybrid of these two approaches is needed.

Here is a design that could achieve the goal of uniformly heating the 10cm x 10cm square with a serpentine pattern.

The serpentine trace is 210cm long and 2mm wide. This is a 1050 square circuit. Dividing the 36.5Ω total resistance by 1050 square leads to a need for a 35mΩ/□ print. Micromax™ silver conductor 5025 could be printed at 10μm thickness to achieve this resistivity. Alternatively, if there was a need to use a less conductive paste, such as PE874, the width of the trace could be increased, the number of segments could be reduced, or multiple print passes could produce the required total resistance.

Another strategy to produce lower total resistance in a long serpentine is to take advantage of connecting multiple resistive elements in parallel. Here an extra lead connection has been added to the center of the serpentine.

This produces two resistive elements connected in parallel. Each element is now half the length of the original, so half as much resistance. The parallel connection of resistive elements is at the core of tile heater designs. In a parallel connection of 2 resistors the total resistance is given by

In the case where the two resistors are equal and half the value of the original series circuit, the total resistance is one quarter the original. In this way we have the option to make narrower or longer traces, or use a much less conductive paste to achieve the same operating parameters. For the general case of some number (N) of resistors connected in parallel, the total resistance is given by.

In the case where all the elements are equal to Ri, this reduces to

This configuration is the basis for design of tile heaters. As a final thought on design for printed wire heaters, think about how the layout will impact uniformity of print thickness, since significant variations will show up as hot and cold spots. This will impact feature size and how changes in trace direction are handled.

Example: Tile Heater (PTC or Fixed Resistance)

Consider a PTC tile heater that will deliver 10W of power when it has reached its design operating temperature of 60C. The PTC resistance magnification factor (RMF) for PTC085 at 60C is about 2.5. So, at room temperature the resistance will be 2.5x lower, so the power will be 2.5x higher, or 25W. We need to design for the room temperature resistance to be appropriate for a 25W heater. In this example we will target an operating voltage of 13.5V. Such a heater must have a total resistance of 7.3Ω (R=V2/P) and will draw a current of1.8A (I=P/V). At typical print thicknesses of about 10μm 5025 silver will have a sheet resistivity (ρ) of 34mΩ/□ and PTC085 will be about 11k Ω/□. Our heater has a 30cm long 10cm wide heated area. There is enough room on either side for a maximum bus width of 1cm with a 1mm space from the edge of the heated area. Leads will be attached on one end of the heater. The interdigitated fingers are 1mm wide. Recall that the total resistance of N identical resistors connected in parallel will be R = Ri/N, where Ri is the resistance of the individual resistors. We know the required total resistance. We will print tiles along the width direction at 50% coverage (c), so th effect will be as though we have a single tile that is half as wide as the width of the heated area, wt = 10cm x 50% = 5cm. Total Resistance R = ρLt/(wt*N). Rearranging, N= ρLt/(wt*R). We also know how long the heater needs to be overall. The length needs to be spanned by N tiles and N+1 finger widths. So Ltotal = NLt + (N+1)wf and we can replace N with the expression ρLt/(wt*R). This can be rearranged into a quadratic equation with a single unknown Lt.

In our example, Lt is 4.5mm and N is 54. Coverage can be adjusted to tune to an exact total resistance while still accommodating an integer number of tiles into the length available.

We could choose to minimize parasitic losses in the bus bars by printing them the full 1cm width the entire length of the heater. But silver can be saved if they are tapered, because as we move along the bus from where the connections are made, the current drops with each tile that is passed. So we could have a linear taper from 1cm to some smaller, practical value at the other end, say 2mm. In our example, about 0.4W will be lost to parasitic losses in the bus if there is no taper. This rises to 0.54W if the taper to 2mm is used. In this and many other practical heater designs, the voltage drop along the length of the bus is not severe and the tiles can be made equal length across the entire heated area. If current is high, or bus width is limited it may be necessary to introduce variable tile width to maintain a constant power density from end to end. Micromax™ can provide guidance with those more advanced calculations. Our example tile heater will be as shown below.

Closing thoughts

Keep in mind that applying protective cover layers, either printed dielectrics/encapsulants or adhesive films will change the resistivity of the printed elements. Some experimentation will be required to learn how to adjust design to compensate. Micromax™ can provide guidance on selection of protective materials and what impact you can expect to see. After working through this design guide, you should be better prepared to understand how materials are selected, how operating conditions of voltage, current, power and resistance are determined, If a tile or printed wire heater is appropriate and even some to the basics of designing a specific geometry to attain the levels of heating power required. You are equipped to understand the choices an experienced expert will make. Seek expert guidance in heater design and keep safety the foremost consideration. Electrical devices carry the risk of electric shock, burns and fire if not properly designed or constructed. Thorough testing of reliability and actual operating temperatures and any associated control and regulating systems must be conducted.