DC Current Source

What is the Stiff DC Current Source? A DC current source is different from the DC voltage source. A constant DC load voltages are produced across different load resistors by DC voltage source but a DC current source is different. A DC current source produces a constant DC current for different load resistors. A simple example of DC current source is a DC battery with a large source resistance as shown in the figure below:

In this circuit, we have assumed that source resistance is 1MΩ. The load current can be found using the following formula:

I_L=\frac{V_S}{R_S+R_L}

where R_L=1Ω

Hence load current is

I_L=\frac{10 \mathrm{~V}}{1 \mathrm{M} \Omega+1 \Omega}=10 \mu \mathrm{A} 

In this case, the load resistance is very small that’s why it has insignificant effect on the load current. Now let’s see the effect of varying the load resistance on the load current. If load resistance is varied from 1Ω to 1MΩ, the following graph is obtained. 

It can be seen that the load current remains constant (10uA) over a large range of resistance ( from 1Ω to 10KΩ). A noticeable drop-off occurs in the load current when load resistance exceeds certain value (10KΩ).

Stiff Current Source

The source resistance of a current source will be ignored when it is 100 times larger than the load resistance. Any current source that satisfies this criteria is called the Stiff Current Source. 

This criteria can be expressed as:

Stiff Current Source: R_S>100R_L

The upper boundary is the worst case. At this point:

R_S =100R_L

When you will solve this expression, you will get the maximum load resistance that can be used for meeting the criteria of stiff current source. 

R_L(max)=0.01 R_S

In other words, we can say that the maximum load resistance=1/100 of the source resistance. When the load resistance equals this worst case value, there is a calculation error is 1% which is small enough to be ignored for calculating the second approximation. So we can conclude that as long as the load resistance is less than 0.01R_S the current source is said to be a stiff current source. 

Also read here

What are the Ideal and Stiff DC Voltage Sources?