Operational amplifiers are frequently used to make highquality current sources in a variety of applications, such as industrial process control, scientific instrumentation, and medical equipment. Single Amplifier Current Sources, published in Analog Dialogue, Volume 1, Number 1, 1967, introduces several current source circuits that provide a constant current through floating loads or grounded loads. In industrial applications, such as pressure transmitters and gas detectors, these circuits are widely used to provide 4mA to 20mA or 0mA to 20mA currents.
The improved Howland current source, shown in Figure 1, is very popular because it can drive a grounded load. The transistor, which allows relatively high currents, can be replaced by a MOSFET to achieve even higher currents. For low cost, low current applications, the transistor can be eliminated, as shown in Difference Amplifier Forms Heart of Precision Current Source, published in Analog Dialogue, Volume 43, Number 3, 2009.
The accuracy of this current source is determined by the amplifier and the resistors. This article shows how to choose the external resistors to minimize errors.
Analysis of the improved Howland current source yields the transfer function:
(1) 
Tip 1: Set R_{2} + R_{5} = R_{4}
In Equation 1, the load resistance influences the output current, but if we set R_{1} = R_{3} and R_{2} + R_{5} = R_{4}, the formula reduces to:
(2) 
Here, the output current is only a function of R_{3}, R_{4}, and R_{5}. With an ideal amplifier, the resistor tolerances determine the accuracy of output current.
Tip 2: Set R_{L} = n × R_{5}
To decrease the total number of resistors in the component library, set R_{1} = R_{2} = R_{3} = R_{4}. Now, Equation 1 simplifies to:
(3) 
If R_{5} = R_{L}, it further simplifies to:
(4) 
Here, the output current depends only on the resistance of R_{5}.
In some cases, the input signal may need to be attenuated. For example, with a 10V input signal and R_{5} = 100 Ω, the output current would be 100 mA. To get a 20mA output current, set R_{1} = R_{3} = 5R_{2} = 5R_{4}. Now, Equation 1 reduces to:
If R_{L} = 5R_{5} = 500 Ω, then:
(5) 
Tip 3: Larger value for R_{1}/R_{2}/R_{3}/R_{4} improves the current accuracy
In most cases, R_{1} = R_{2} = R_{3} = R_{4}, but R_{L} ≠ R_{5}, so the output current is as shown in Equation 3. With R_{5} = 100 Ω and RL = 500 Ω, for example, Figure 2 shows the relationship between the resistance of R_{1} and the current accuracy. To achieve 0.5% current accuracy, R_{1} must be at least 40 kΩ.
Tip 4: Resistor tolerance affects current accuracy
Real world resistors are never ideal, with each having a specified tolerance. Figure 3 shows an example circuit, where R_{1} = R_{2} = R_{3} = R_{4} = 100 kΩ, R_{5} = 100 Ω, and R_{L} = 500 Ω. With the input voltage set to 0.1 V, the output current should be 1 mA. Table 1 shows the output current error caused by different resistor tolerances. To obtain 0.5% current accuracy, choose 0.01% tolerance for R_{1}/R_{2}/R_{3}/R_{4}, 0.1% for R_{5}, and 5% for R_{L}. Resistors with 0.01% tolerance are expensive, so a better choice would be to use an integrated difference amplifier, such as the AD8276, which has better resistor matching and is more cost effective.
Table 1. Worst Case Output Current Error (%) vs. Resistor Tolerance (%)
Resistor Tolerance/
Resistors Varied

5  1  0.5  0.1  0.05  0.01  0 
R_{1}/R_{2}/R_{3}/R_{4}  110.11  10.98  5.07  1.18  0.69  0.30  0.20 
R_{5}  5.05  1.19  0.70  0.30  0.25  0.21  0.20 
R_{L}  0.21  0.20  0.20  0.20  0.20  0.20  0.20 
Conclusion
When designing an improved Howland current source, choose external resistors to make the output current independent of the load resistance. Resistor tolerance influences the accuracy, and a tradeoff between accuracy and cost must be made. The amplifier’s offset voltage and offset current will also affect the accuracy. Consult the data sheet to check if the amplifier can meet the circuit requirements. Multisim can be used to simulate how these specifications influence the accuracy. An integrated difference amplifier—with its low offset voltage, offset voltage drift, gain error, and gain drift—can cost effectively implement accurate, stable current sources.
References
Guo, David. LowPower, UnityGain Difference Amplifier Implements LowCost Current Source , Analog Dialogue, Volume 45, Number 2, 2011.
Loe, James M. Groundedload current source uses one operational amplifier, Analog Dialogue, Volume 1, Number 3, 1967.
Miller, Bill. Single Amplifier Current Sources, Analog Dialogue, Volume 1, Number 1, 1967.
Moghimi, Reza. Ways to Optimize the Performance of a Difference Amplifier, AN589.
Zhao, Neil, Reem Malik, and Wenshuai Liao. Difference Amplifier Forms Heart of Precision Current Source, Analog Dialogue, Volume 43, Number 3, 2009.