Analysis of Cascode configuration Amplifier

[BenBa]

Homework Statement

Homework Equations

See above picture.

The Attempt at a Solution

I am stuck on the first part, i know i need to find the x intercept of the DC load line is at +Vcc, and I am pretty sure the y intercept is at Vcc/R7, but I do not know how to use this information to find the Q point.

The Q point is the current and Vce drop when there is no input signal. So i think i am supposed to assume that Vin is 0V and see what that gets me.

Well if Vin is zero volts then Vb of Q1 is 0V which means Ve of Q1 is -0.7 volts. From this we can find the current through R5 because the it should equal (-0.7 - -Vcc)/R5. I am now wondering if that means the the current through R4 is also this amount because the collector current is approximately the same as the emitter current. But i have no idea, furthermore i don't know how to use this information to help me determine the Q point of Q3 (i am really just spitballing).

Any help is much appreciated!

EDIT: So i believe i have a different approach to solving part a. If we assume negligible current goes into the base of each transistor we can use a voltage divider to find the voltage at the base of Q1, this would be Vcc *[R3/(R1+R2+R3)], let's call this Vb. Now we use the standard diode drop 0.7 to find the voltage of the emitter. Then using the above method for finding current through the emitter resistor of the Q1 we find that Ie = (Vb-0.7-(-Vcc))/R4. So this is the current through the emitter resistor. I don't know if we can assume this is also the current through the collector resistor of Q1, but if it is we can simply find the voltage at the collector of Q2 via Vcc - Ie*R4.

This gives us the voltage before R6. But now i don't know where to go...also i don't know if this second method i used is the correct one, but it makes more sense to me that the first one wrote down.

 

[rude man]

Homework Statement

Homework Equations

See above picture.

The Attempt at a Solution

EDIT: So i believe i have a different approach to solving part a. If we assume negligible current goes into the base of each transistor we can use a voltage divider to find the voltage at the base of Q1, this would be Vcc *[R3/(R1+R2+R3)],

Incorrect. The bottom of R3 does not go to ground. Fix this up.

Lets call this Vb. Now we use the standard diode drop 0.7 to find the voltage of the emitter. Then using the above method for finding current through the emitter resistor of the Q1 we find that Ie = (Vb-0.7-(-Vcc))/R4.

You mean R5.

So this is the current through the emitter resistor. I don't know if we can assume this is also the current through the collector resistor of Q1,

You mean Q2.
Why wouldn't you? alpha = 1.

but if it is we can simply find the voltage at the collector of Q2 via Vcc - Ie*R4.

Good to here.

This gives us the voltage before R6. But now i don't know where to go...also i don't know if this second method i used is the correct one, but it makes more sense to me that the first one wrote down.

You're OK once you fix your early problems.

The rest should be easy. What does R6 really do? (Hint: very little).

So then what is the dc voltage at Q3-b and Q3-e? The you're done.

 

[BenBa]

I have never used a voltage divider when it doesn't got to ground... I am unsure how to do this. Would it be $V_b = \frac{[Vcc-(-Vcc)]R_3}{R_1+R_2+R_3} = \frac{2VccR_3}{R_1+R_2+R_3}$

Yes i meant R5, so $I_{Q1e} = \frac{V_b}{R_5}$

I don't know what alpha you are referring to. I didn't know we could assume the current through $I_{Q1e}$ was the same down the entire line of collectors and emitters because I feel like some of the current has to split off such as through R6 and into the base of each transistor, but i know the current into the trasistor is negligble, what i do not know is if the current into R6 is negligible.

by the way, thanks so much for your help!

So using what we know we can solve for the current through the emitter resistor of Q3, does that give us the quiescent current right away? And also we know the Vce of Q3 since we can find out Ve of Q3.

I am not sure what R6 actually does in this circuit, if its negligible why do we even have it?

For part b what does it mean by 'maximum mid-frequency input' so the output is undistorted? Are they asking me to find the AC load line?

 

[rude man]

I have never used a voltage divider when it doesn't got to ground... I am unsure how to do this. Would it be $V_b = \frac{[Vcc-(-Vcc)]R_3}{R_1+R_2+R_3} = \frac{2VccR_3}{R_1+R_2+R_3}$

No, that would be correct if the low side went to ground and the high side were 2Vcc.

You need to solve this using KCL or KVL or whatever. I personally sum currents to zero at every independent node which is close to KVL but not quite.

Yes i meant R5, so $I_{Q1e} = \frac{V_b}{R_5}$

I don't know what alpha you are referring to. I didn't know we could assume the current through $I_{Q1e}$ was the same down the entire line of collectors and emitters because I feel like some of the current has to split off such as through R6 and into the base of each transistor, but i know the current into the trasistor is negligble, what i do not know is if the current into R6 is negligible.

Alpha is ic/ie. If ib = 0, ic = ie.

Unless you are given a 'trick' question, if it's a linear circuit assume ALL base currents are zero (unless the instructor orders otherwise). You made the right decision to let all ib = 0 so why are you questioning it now? No current can pass through R6 because that would mean a finite base current for Q3.

So using what we know we can solve for the current through the emitter resistor of Q3, does that give us the quiescent current right away? And also we know the Vce of Q3 since we can find out Ve of Q3.

Yes. Quiescent currents and voltages everywhere.

I am not sure what R6 actually does in this circuit, if its negligible why do we even have it?

We "have it" because someone has a share in a resistor company and wants them to sell lots of unneeded resistors.

For part b what does it mean by 'maximum mid-frequency input' so the output is undistorted? Are they asking me to find the AC load line?

The input filter is a high-pass so low frequencies have low gain. At some frequency f₀ the gain is 3 dB below the "high-frequency" gain. At frequencies >> f₀ the transistors themselves start to roll off gain.

For part (b) you can simply assume C2 to be infinitely large, use any frequency you like and ignore the high-frequency transistor rolloff. Your job is to compute the voltage at every node in the circuit and determine when clipping of the sine wave occurs at anyone of them. The corresponding input voltage is the answer to part (b).

For part (c) you will need to compute f₀ among other things.

 

[BenBa]

The input filter is a high-pass so low frequencies have low gain. At some frequency f₀ the gain is 3 dB below the "high-frequency" gain. At frequencies >> f₀ the transistors themselves start to roll off gain.

For part (b) you can simply assume C2 to be infinitely large, use any frequency you like and ignore the high-frequency transistor rolloff. Your job is to compute the voltage at every node in the circuit and determine when clipping of the sine wave occurs at anyone of them. The corresponding input voltage is the answer to part (b).

For part (c) you will need to compute f₀ among other things.

Sorry but I am confused what to do for part b. You said assume the input capacitor are infinitely large? So no matter the frequency it is always cut off? How does that help us? And what do you mean by "roll off" of the transistors.

Are you suggesting i need to calculate the AC load lines for each transistor?

Thanks again for the help!

 

[BenBa]

Also how would we approach this problem if we didn't assume that the current going into the base of the transistors is negligible? Would it be much harder to calculate the new base voltage?

 

[rude man]

Sorry but I am confused what to do for part b. You said assume the input capacitor are infinitely large? So no matter the frequency it is always cut off?

It's a high-pass, not a low-pass. So all frequencies ABOVE f₀ get through. Frequencies BELOW f₀ get cut off.

And what do you mean by "roll off" of the transistors.

I mean if the frequency is REALLY large, like >> f₀, then the transistors with their little "built-in" capacitors reduce the gain all by themselves.

Are you suggesting i need to calculate the AC load lines for each transistor?

Thanks again for the help!

Never mind load lines. I never use them. You don't need load lines unless your instructor tells you to come up with one.

 

[BenBa]

So how exactly do i go about calculating f0 for this circuit? And what does that tell me about the mid-frequency voltage?

And is it effected by the fact that i am supposed to not ignore the current going into the bases of the transistors?

 

[rude man]

So how exactly do i go about calculating f0 for this circuit? And what does that tell me about the mid-frequency voltage?

Assume the mid-frequency is 10 f0.

To calculate f0, consider C1 a short circuit for f0.

So what kind of voltage divider do C2, R2 and R3 make? I mean, what is the cutoff frequency f0?
Use KVL etc. if you have to.

 

[BenBa]

Why do we assume mid-frequency is 10 f0? What exactly is "mid-frequency"?

I'm sorry but I don't quite understand what you mean by a voltage divider of C2, R2, and R3?

 

[rude man]

Why do we assume mid-frequency is 10 f0? What exactly is "mid-frequency"?

I'm sorry but I don't quite understand what you mean by a voltage divider of C2, R2, and R3?

Look up "high-pass RC network" on the Web. Then remember what I said: C1 looks like a short to ac. Also, of course, so does -Vcc.

Then I have to let you figure it out for yourself because otherwise I'd be doing the whole shebang for you.

"Mid-frequency" in this context is a frequency well above f0 but not so high as to have the transistors reduce the gain by themselves. I picked 10f0. As far as you're concerned, 'mid-frequency' and 'high-frequency' mean the same thing here because you're fortunately not asked to take th high-freq. response of the transistors into account.

If you had to include finite base currents the work would be a lot more tedious. Freq. response would not be affected, neither would gain.

Any circuit where beta is important is a crummy circuit because beta can vary by 5:1 for a given transistor type, not to mention temperature sensitivity.

 

[BenBa]

I looked up high pass RC network and it just gave me a simple RC passive filter. If C1 is a short to AC then the voltage divider at the node between C2, R2, and R3 is a low pass filter? How does that help us determine the frequency that causes distortion?

 

[rude man]

I looked up high pass RC network and it just gave me a simple RC passive filter. If C1 is a short to AC then the voltage divider at the node between C2, R2, and R3 is a low pass filter? How does that help us determine the frequency that causes distortion?

Why do you persist in saying "low-pass filter"?

The filter from the input to the base of Q1 is a high-pass filter.

And you're misquoting the question; it asks for the max. input voltage amplitude, not the frequency that causes distortion.

 

[BenBa]

Ah, i see now, sorry!

I am just confused how to start with this question. I know you asked what kind of voltage divider C1, R2, and R3 create, but dividing between what two points?

 

[rude man]

Ah, i see now, sorry!

I am just confused how to start with this question. I know you asked what kind of voltage divider C1, R2, and R3 create, but dividing between what two points?

What does a high-pass R_C filter look like?

 

[BenBa]

A capacitor and a resistor in series, with voltage out taken in between, right?

 

[rude man]

A capacitor and a resistor in series, with voltage out taken in between, right?

Yes, but where is the R and where is the C?
Where is the input, where is the output, and what goes to ground?

 

[BenBa]

Input is connected to capacitor, then to resistor, then to ground.

In my circuit the input is at Vin, it passes the capacitor and then the current splits, some goes up to R2 and some into the base of Q1, and some down to R3. None of it goes to ground it seems, but i suppose that doesn't really matter since its just a potential like any other.

 

[rude man]

Input is connected to capacitor, then to resistor, then to ground.

In my circuit the input is at Vin, it passes the capacitor and then the current splits, some goes up to R2 and some into the base of Q1, and some down to R3. None of it goes to ground it seems, but i suppose that doesn't really matter since its just a potential like any other.

Both R2 and R3 go to ground. AC ground! What is "ground"? It's just volts = 0. What is the ac voltage at the other ends of R2 and R3?

Your statement about "... a potential like any other" makes no sense to me.

The base of Q1 does not count. It looks like a very high resistor to both ac and dc. There is no current into Q1-b, either ac or dc.

While I'm at it I might as well give my lecture on the important distinction between ac and dc parameters. I urge you to always use caps for dc and lower-case for ac quantities.

So actually it should be v_in, not V_in, for example. The dc gain V_out/V_in = 0 thanks to C2.

 

[BenBa]

Ah! That makes so much sense! because constant voltage sources are ground in AC analysis!

Okay so if the voltage drops to ground over both R2 and R3 doesn't that mean that mean that that the currents through R2 and R3 are different? because the resistor values are different. I'm sorry but I don't quite see how this gets us closer to finding the maximum mid frequency voltage?

 

[rude man]

Ah! That makes so much sense! because constant voltage sources are ground in AC analysis!

Okay so if the voltage drops to ground over both R2 and R3 doesn't that mean that mean that that the currents through R2 and R3 are different? because the resistor values are different. I'm sorry but I don't quite see how this gets us closer to finding the maximum mid frequency voltage?

How about R2 and R3 are in parallel to form your high-pass with C2?

If you got that then you have the voltage at the base of Q1. Then you can propagate the signal all the way to the output.

Your max. allowable vltage is when the signal is "clipped" anywhere along the circuit. That means when any of the transistors reach Vce < Vbe. One way to do this in this case would be to write an equation for Vce for each transistor as a function of the dc voltage at Q1-b.

 

[BenBa]

R2 and R3 are in parallel to form an RC high pass filter with cutoff frequency 1/(2*pi*(R2||R3)*C2) = 6021.81 Hz. So any signals smaller than this will be chopped off, is this the f0 of the entire circuit though?

 

[rude man]

R2 and R3 are in parallel to form an RC high pass filter with cutoff frequency 1/(2*pi*(R2||R3)*C2) = 6021.81 Hz. So any signals smaller than this will be chopped off, is this the f0 of the entire circuit though?

You got the time constant of the input hi-pass filter right, but you're missing the point about clipping.

To study clipping you input a signal at say 10f₀ or ~ 60 KHz. You increase the input voltage and look at the emitters and collectors of all three transistors. At some level of input voltage, one of these nodes will look like a "clipped" sine wave, which is a sine wave with the top, bottom or both flattened. As soon as you get any flattenting, that's the max. input voltage you can tolerate.

As I said before, an easy way is to enforce a dc input at the base of Q1, bypassing the hi-pass altogether, and look at the aforementioned nodes. At some level of dc voltages (you have to go above and below the quiescent Q1-b voltage), Vce will be < Vbe and that's where you have to stop. Do this in both directions and you have the max. peak-to-peak input voltage you can tolerate.

 

[BenBa]

To study the clipping does that mean i need to draw the AC load lines for Q1 and Q2 and Q3 and see if the voltage hits saturation or the x axis? I feel like that's a really long way to find where clipping occurs.

Also so the cascode configuation passes high frequencies from the high pass filter formed with C2, R2, and R3. Where does the low pass filtering come in? Cascode configuration is supposed to have a bandpass, right?

 

[rude man]

To study the clipping does that mean i need to draw the AC load lines for Q1 and Q2 and Q3 and see if the voltage hits saturation or the x axis? I feel like that's a really long way to find where clipping occurs.

As I said, I don't use load lines, don't even know for sure how to generate them. Just vary the dc voltage at Q1-b up & down, compute the voltages at all e and c nodes as functions of Q1-b voltage, and when anyone of them is limited by +/-Vcc or ground or Vce < Vbe, the you've found the limit of input voltage.

Also so the cascode configuation passes high frequencies from the high pass filter formed with C2, R2, and R3. Where does the low pass filtering come in? Cascode configuration is supposed to have a bandpass, right?

The basic cascode configuration is designed to NOT have a bandpass response, to as high a frequency as possible. It's designed to have as flat a frequency response over as wide a frequency band as possible. Your problem states that right off the bat. This is a high-pass circuit only because of C2, R2 and R3. But all circuits roll off their frequency response if the frequency is high enough. In your case the transistors determine the high cutoff frequency.

When coming up with the Bode plot, concentrate on the high-pass pole formed by C2, R2 and R3 (~6 KHz). You can show a flattening and subsequent rolloff at some high frequencies like 3 and 10 MHz.