Design formulas simplify classic V/I converter
Dudley Nye, Nye Engineering Co, Fort Lauderdale, FL -- EDN, January 20, 2000
Figure 1 shows a classic voltage-to-current (V/I) converter. You can select the resistor values such that the output current in the load, RL, varies only with the input voltage, VIN, and is independent of RL. The circuit is widely used in industrial instruments for supplying a 4- to 20-mA signal. The circuit has its limitations, however, because the resistor values must be quite accurate to obtain a true current source. The literature describing the circuit provides design methods that are for special cases or are for approximate designs. This Design Idea gives two simple design formulas you can use to determine the component values that produce a true current source. It also provides a general formula for the output current, IL, for any selection of resistor values, not just the constant-current selection.
For a true current output, IL, as a function of the input voltage, VIN, you must satisfy the following two equations:
In Equation 1, you can arbitrarily select any four of the terms and then determine the fifth term by solving the resulting equation. In Equation 2, you can arbitrarily select either R3 or R4 and then determine the unselected resistor after substituting the applicable terms from Equation 1. For example, you can solve Equation 1 for R2 when IL=20 mA, R1=100 kW, RX=0.1 kW, and VIN=4V yields R2=49.9 kW. Now, let R4=100 kW and, with Equation 2, solve for R3 as follows: R3=(49.9 kW+0.1 kW)=50 kW. This example configures a design for the popular current source of 4 to 20 mA. In a second example, if RX changes from 100 to 400W, the feedback changes fourfold, and you would expect that the output current would change fourfold, to 1 to 5 mA. You can check the result by substituting in the general formula for the output current:
When the complete coefficient (the terms inside the square brackets) of RL equals zero, a true current source results, and equations 1 and 2 are valid. Note that substituting the values from the first example above forces the coefficient to zero. Substituting the values from the second example above results in the following expression:
With RL=0.2 kW and VIN=4V, IL=5.019 mA. Then, with VIN=0.8V, IL=1.003 mA. Thus, after changing the feedback resistor by 4-to-1, you still have currents close to the 1- to 5-mA standard. Note also that IL=5.02 mA when RL=0W; thus, the circuit is still almost a perfect current source. This result is unique, as you can convert from 4 to 20 ma to 1 to 5 mA by changing only one resistor. You can configure the less used standard of 10 to 50 mA by making RX=100/2.5=40W. (DI #2471)
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R4 was missed intentionally to hide his idea. And will not pay attention to any reader's comment.
Henry Maquinad - 2010-25-2 04:13:00 PST -
Regarding the missing R4 in the diagram:
Cyril Mechkov is correct. This circuit is a Howland current pump, and R4 should be shown connected from the inverting input to ground.
Norman Lind - 2009-12-8 09:17:00 PDT -
where is R4 in the diagram?!
Robert Dodde - 2009-9-3 09:35:00 PDT -
I have spent a lot of time to reveal the idea behind this strange circuit of a voltage-to-current converter (this is my pursuit, see www.circuit-fantasia.com).
This morning I finally realized that it is a version of the famous Howland current source (pump) where the idea is keeping a constant current by adding an additional "helping" current.
Only, I have also realized that this circuit can't work properly with the op-amp voltage follower shown; it needs some gain. Therefore, we need a non-inverting amplifier; that means to connect a resistor (the missing R4) between the inverting input and the ground.
Actually, the circuit discussed is a negative resistor implemented as a "helping" current source connected in parallel to the load - see the Wiki article about negative resistance.
By the way, I have not managed to find out this "wideley used" circuits by Google. Also, I have not managed to open the equations by my browser.
If you want to discuss more this circuit, please email me.
Cyril Mechkov - 2007-11-4 22:59:00 PDT -
Hello Sir, I wish to know where is R4 resistor in the figure. You mentioned about R4 in circuit eqaution (2). Please let me know.
Thanks and Regards
Pratap
Pratap Kollu - 2006-13-12 05:40:00 PST
