Determining the Equivalent Series Resistance (ESR) of Capacitors
Learn more about the importance of capacitor ESR, how to measure it, and what factors can affect your measurements.
As operational frequencies increase and electronic systems become more complex and smaller, designers must pay close attention to capacitor ESR because it influences power usage and efficiency.
Knowing the ESR value at expected operating conditions can greatly help in determining the suitability of a particular capacitor to perform a given function.
Some manufacturers specify the ESR at a particular frequency and operating conditions, some just define the dissipation factor, and others provide neither the ESR nor the dissipation factor.
Equivalent series resistance (ESR) is one of the non-ideal characteristics of a capacitor which may cause a variety of performance issues in electronic circuits. A high ESR value degrades the performance due to I2R losses, noise, and higher voltage drop.
In some applications, the heat generated due to ESR is small and may not be an issue. However, in some circuits, particularly high-current applications, the heat dissipated may cause a significant temperature rise, affect the operation of the circuit, and degrade the capacitor. In addition, a significant amount of voltage drop occurs across the resistance, reducing a portion of the useful energy in the application.
As such, capacitor selection for applications such as RF, energy harvesting, filter circuits, and other sensitive circuits, requires consideration of other characteristics beyond the capacitance and voltage values.
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Effects of ESR on RF and Energy Harvesting Circuits
Even though the ESR for ceramic capacitors is very small, on the order of milliohms, the resistance can significantly affect circuits such as RF and low power circuits.
In hand-held RF transmitters, high ESR capacitors in the drain coupling or source bypassing stages of the amplifier would consume and waste more battery power due to the higher I2ESR losses. This would reduce the efficiency, power output, and battery life.
Also, most of the RF semiconductor devices made for the matching stages are built with very low input impedances. As such, a matching capacitor such as a Multilayer Ceramic Chip Capacitor (MLCC) with a high ESR would represent a notable percentage of the overall network impedance. For example, if the input impedance of the device is 1 ohm, a matching capacitor with an ESR of 0.8 ohms will dissipate about 40 percent of the total power, hence decreasing the output power and circuit efficiency.
Capacitors in energy harvesting applications provide more critical roles of accumulating the charge from low voltage energy sources and quickly and efficiently discharging this stored energy to power the load. The capacitors and other components in the energy harvesting circuits should, therefore, consume very little power during operation.
A high-ESR capacitor would have more I2ESR losses, such that some of the captured energy will end up being wasted as heat, hence decreasing the energy output of the capacitor. However, designers may prefer supercapacitors (despite their higher ESR and leakage) because they offer higher energy densities.
Determining ESR Using an ESR Meter
The ESR meter is a moderately accurate instrument that is affordable and convenient to use, especially when measuring several capacitors while they are still in the circuit. An alternating voltage is applied to the capacitor in a voltage divider network configuration. The frequency of the applied AC is usually a value at which the capacitor’s reactance is negligible.
Figure 1. A simple model of ESR measurement. Image courtesy of Kerry Wong.
During the test using an ESR meter, a current is passed through the capacitor for a very short time such that the capacitor doesn’t charge completely. The current produces a voltage across the capacitor. This voltage will be the product of the current and the ESR of the capacitor plus a negligible voltage due to the small charge in the capacitor.
Since the current is known, the ESR value is calculated by dividing the measured voltage by the current. The results are then displayed on the meter readout.
ESR tests can be performed when the capacitor is in the circuit or out of the circuit. For capacitors connected in parallel, the measurement gives the overall resistance. The specific capacitors must be removed if their individual ESR is to be determined. However, if there are hundreds of capacitors, it is tedious to remove each capacitor, and there is an increased risk of damaging the capacitors or the circuit board during the removal.
A typical ESR meter uses a high-frequency current of about 100 kHz and a low voltage of about 250 mV or less. The low voltage is insufficient to bias and activate the semiconductor devices in the surrounding circuitry, ensuring that the impedance of the nearby components does not impact the ESR reading.
The capacitor should be discharged before the measurement. Some ESR meters have a built-in discharge mechanism. However, it may be important to discharge the capacitor manually, especially if it is a high voltage cap whose charge can damage the ESR meter.
Even though an ESR meter can comfortably test in-circuit capacitors, it has frequency limitations as well as a lowest resistance level that it can accurately measure.
Coaxial Resonant Tube Measurement for Ultra-low Resistances at High Frequencies
Since the ESR value is dependent on the operating frequency, measuring ultra-low ESR values at very high frequencies becomes a challenge when using conventional ESR meters.
For ceramic capacitors, the most accurate method of determining ESR at high frequencies (100 MHz to 1.3 GHz) is the coaxial resonant line method. This technique is based on the Boonton model 34A standard and used along with an RF signal generator and an RF voltmeter.
Figure 2. Coaxial resonant tube block diagram. Image courtesy of Knowles Capacitors (PDF).
The coaxial resonator line is made of copper tubing with a solid copper rod as the center conductor. The capacitor under test is placed in series between the center conductor and the ground conductor.
The unloaded characteristic of the resonator line must first be determined before carrying out the ESR measurement on the capacitor. An RF excitation to the shorted coaxial line helps to determine the λ/4 and 3λ/4 bandwidth, while the λ/2 and λ bandwidth is established when the line is open circuited (λ refers to the wavelength; see this article for related information). This data characterizes the resonant frequency, the unloaded Q of the resonant line, and the fixture resistance.
The capacitor to be tested is then placed in the DUT (device under test) section, and the signal generator is tuned for the peak resonant voltage. The capacitor causes a change in the resonant frequency and the Q factor, whose values are now different from those of the unloaded coaxial line. Transmission line calculations are employed, and the ESR value is determined based on the relationship between the new frequency and Q factor and the frequency and Q factor of the initial unloaded condition.
Figure 3. Bandwidth of loaded and unloaded transmission line. Image courtesy of American Technical Ceramics (PDF).
Nowadays, it is common practice to use a vector network analyzer to replace both the signal generator and the RF voltmeter. With a VNA, the resonant frequency is read off from the display. Some VNA models can export the results directly to a calculation program and display the final ESR value.
The tube length is designed to work in the frequency range of about 100 MHz to 1.5 GHz; however, custom lengths can be made for frequencies outside this range.
Factors that Affect ESR Measurements
ESR measurement errors may occur as a result of problems with the technique, how the contact or interface to the capacitor is made, or lack of measurement-equipment calibration.
The resistances, self-induction, and capacitance of the measurement instrument and its leads must be taken into account, particularly at high measuring frequencies.
Test Leads Resistance and Inductance
The resistance of test leads is a common source of error in low-resistance measurements. The resistance adds to the DUT resistance.
In addition, self-retracting, spiral-wound test leads should be avoided since their inductance can be an error source.
Interference from Nearby Equipment
The measurement should be performed in areas far away or shielded from sources of significant EMI (electromagnetic interference). Otherwise, the test leads could pick up interference, and this could affect the readings.
ESR varies according to capacitor type and operating conditions such as frequency and temperature. Some manufacturers specify ESR at a particular frequency and under certain operating conditions, others just give the dissipation factor, and others do not provide either ESR or dissipation factor. However, knowing the ESR value under expected operating conditions can greatly help in determining the suitability of a particular capacitor for performing a given function.
The type of method used to determine ESR depends on factors such as the type of capacitor, the operating frequency, and the required precision. While an ESR meter and other DIY measurements are adequate for a number of applications at frequencies up to about 100 kHz, they cannot accurately determine very low ESR values at very high frequencies. The coaxial resonant line method is often preferred when determining ultra-low ESR values at frequencies between approximately 100 MHz and 1.3 GHz.
As operational frequencies increase and electronic systems become smaller and more complex, close attention must be paid to parameters such as ESR, which directly influences circuit performance and power efficiency.