Designing a band pass filter using given specifications

Question

I am trying to design a band pass filter using the below emitter follower circuit : enter image description here

The Specifications for the filter include : $$ Z_{in} = 16k\Omega \\ \text{Current gain} = 35dB \\ \text{3dB bandwidth} = 418kHz$$

I am allowed to vary \$R_2 , V_{cc}, C_{1} , C_{2}\$ to achieve my specification.

I used the T-model of the amplifier and tried to solve for the collector current using the equation $$A_{i} = \frac{(\beta+1).Z_{in}}{r_{\pi}}$$ where $$r_{\pi} = \frac{V_{T}.\beta}{I_{c}}$$ Using \$\beta = 381.7 , V_{T} = 26mV \; \text{,i am getting} \; I_{c} = 91\mu A\$

Using the above value of \$r_{\pi}\$ , I Plug it in : $$ \frac{1}{Z_{in}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{r_{\pi}}$$

Putting the value of \$R_{1}\; \text{and}\; r_{\pi} \;\text{gives me}\; R_{2} = 28k\Omega\$

However , when I do a small signal ac analysis in Ltspice using the value found for \$R_{2}\$ and a sinusoid of frequency 1kHz for a duration of 5ms and \$V_{cc} = 12\$ I am getting the collector current in picoamperes.

What mistake have I actually made in finding \$R_{2}\$ and what procedure should be followed to meet the required specifications ?

• a concerned citizen: I didn't calculate, but if you compare the resulting 22 Ohms vs the other values for the resistors, what do you see? Did you mean KOhms?
• Starboy: made the necessary edits

Answer 1

C1 is the only reasonable way of achieving the lowpass portion of the specification ... in the given schematic.

As Andy says. it's such an odd way of achieving the goal that it looks like a mistake.

Further, when we look at the specification ... we are given an -3dB bandwidth but no centre frequency, therefore the problem is under-specified.

So, pick any lower -3dB frequency (call it F1) you want, and design the high pass element (C1 and the input impedance Zin, given as 16k) to meet that frequency.

Then pick F2 = F1 + 418kHz, and design the low pass element (transistor output impedance and C2) to meet that.

It's a lousy design without a complete specification but that's the assignment.

Answer 2

Your very big mistake is the capacitor on the output: -

enter image description here

I can't tell you why the collector current is so poor but, I can tell you the above circuit shouldn't have the capacitor (C1) connected like that.

Try putting a fixed value for R2 in case your math is wrong. Maybe also choose R2 so that you get around half supply voltage at the base.

• Henning Larsen: well, the question is not clear. It specifies current gain but does not specify current through where? Diagram suggests C1. It may still be a valid circuit if C1 represents the load. A piezo transducer for instance.
• Andy aka: @hanning have you come across a 10 iF piezoelectric device been driven by such a low power and ancient transistor before?