I'm trying for a year now to understand this and no matter how good I am at solving amplifier circuits at my University I still can't
figure this out. This is what I'm talking about:
In all my experiments I assume \( V_{BE} = 0.7V \) because it seems to work and I do the calculations using
\( R_{1} = \frac{V_{cc}V_{b}}{I_{b}} \) , \( R_{2} = \frac{V_{cc}V_{c}}{I_{c}} \) , \( I_{b} = \frac{I_{c}}{B} \)
First try:
\( V_{c} = 0 \) , \( I_{c} = 100mA \) , \( B = 10 \)
\( R_{2} = \frac{100}{100mA} = 100 Ohms\) , \( I_{b} = \frac{100mA}{10} = 10mA \) , \( R_{1} = \frac{100.7}{10mA} = 930Ohms \)
And it works:
Second try:
\( V_{c} = 0 \) , \( I_{c} = 100mA \) , \( B = 800 \) (Max Hfe for BC547C)
\( R_{2} = \frac{100}{100mA} = 100 Ohms\) , \( I_{b} = \frac{100mA}{800} = 0.125mA \) , \( R_{1} = \frac{100.7}{0.125mA} = 74.4k \)
And it doesn't work. Ib is the same as my calculations but Ic and Vc that I requested are different.
Third try:
The previous probably didn't work because the following values can not exist at the same time when the transistor is operating:
\( V_{c} = 0 \) , \( I_{c} = 100mA \) , \( B = 800 \) (Max Hfe for BC547C)
Now, what if I try to figure out the MAX Hfe that I can choose for \( I_{c} = 100mA \)?
\( V_{c} = 0 \) , \( I_{c} = 100mA \) , \( B = ? \)
The graph is telling me that for 100mAdc the max value of Hfe is 0.6 (normalized value) which means that any <= 0.6
should work with that current as long as there is a resistor in the collector. Of course if the transistor is operating by itself there is only
one value Hfe = 0.6 for a Ic = 100mA
\[ H_{fe} = B = H_{fe_{normalized}} \cdot [max  min] + min = 0.6 \cdot [800  420] + 420 = 648 \]
\( R_{2} = \frac{100}{100mA} = 100 Ohms\) , \( I_{b} = \frac{100mA}{648} = 0.15mA \) , \( R_{1} = \frac{100.7}{0.15mA} = 62k \)
And it doesn't work:
Again Ib is what I predicted with my math, but everything else is not!!!
The problem is definetly that these linear formulas:
\( R_{1} = \frac{V_{cc}V_{b}}{I_{b}} \) , \( R_{2} = \frac{V_{cc}V_{c}}{I_{c}} \) , \( I_{b} = \frac{I_{c}}{B} \)
mathematically speaking can take any range of values (except not zero in the denominator of course).
The reality though, is that the transistor is not linear and I must choose the values in such a way that they can "happen together".
How do I figure this out?
Thanks!
PS:
From my first try, you can see that I use Hfe = 10 and the LTspice is showing that this can happen since the circuit works as my math told me.
So what does the datasheet mean by these Hfe values:
Clearly from my experiments, I can have Hfe values less than 420.
figure this out. This is what I'm talking about:
In all my experiments I assume \( V_{BE} = 0.7V \) because it seems to work and I do the calculations using
\( R_{1} = \frac{V_{cc}V_{b}}{I_{b}} \) , \( R_{2} = \frac{V_{cc}V_{c}}{I_{c}} \) , \( I_{b} = \frac{I_{c}}{B} \)
First try:
\( V_{c} = 0 \) , \( I_{c} = 100mA \) , \( B = 10 \)
\( R_{2} = \frac{100}{100mA} = 100 Ohms\) , \( I_{b} = \frac{100mA}{10} = 10mA \) , \( R_{1} = \frac{100.7}{10mA} = 930Ohms \)
And it works:
Second try:
\( V_{c} = 0 \) , \( I_{c} = 100mA \) , \( B = 800 \) (Max Hfe for BC547C)
\( R_{2} = \frac{100}{100mA} = 100 Ohms\) , \( I_{b} = \frac{100mA}{800} = 0.125mA \) , \( R_{1} = \frac{100.7}{0.125mA} = 74.4k \)
And it doesn't work. Ib is the same as my calculations but Ic and Vc that I requested are different.
Third try:
The previous probably didn't work because the following values can not exist at the same time when the transistor is operating:
\( V_{c} = 0 \) , \( I_{c} = 100mA \) , \( B = 800 \) (Max Hfe for BC547C)
Now, what if I try to figure out the MAX Hfe that I can choose for \( I_{c} = 100mA \)?
\( V_{c} = 0 \) , \( I_{c} = 100mA \) , \( B = ? \)
The graph is telling me that for 100mAdc the max value of Hfe is 0.6 (normalized value) which means that any <= 0.6
should work with that current as long as there is a resistor in the collector. Of course if the transistor is operating by itself there is only
one value Hfe = 0.6 for a Ic = 100mA
\[ H_{fe} = B = H_{fe_{normalized}} \cdot [max  min] + min = 0.6 \cdot [800  420] + 420 = 648 \]
\( R_{2} = \frac{100}{100mA} = 100 Ohms\) , \( I_{b} = \frac{100mA}{648} = 0.15mA \) , \( R_{1} = \frac{100.7}{0.15mA} = 62k \)
And it doesn't work:
Again Ib is what I predicted with my math, but everything else is not!!!
The problem is definetly that these linear formulas:
\( R_{1} = \frac{V_{cc}V_{b}}{I_{b}} \) , \( R_{2} = \frac{V_{cc}V_{c}}{I_{c}} \) , \( I_{b} = \frac{I_{c}}{B} \)
mathematically speaking can take any range of values (except not zero in the denominator of course).
The reality though, is that the transistor is not linear and I must choose the values in such a way that they can "happen together".
How do I figure this out?
Thanks!
PS:
From my first try, you can see that I use Hfe = 10 and the LTspice is showing that this can happen since the circuit works as my math told me.
So what does the datasheet mean by these Hfe values:
Clearly from my experiments, I can have Hfe values less than 420.
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