Dr. T (Tamara Schmitz): Hey, Dave. What are you doing? Thinking about the good old days?

Dave (Dave Ritter): Actually, yes, you caught me daydreaming about old flames.

Dr. T: Really? Tell me more.

Dave: Not those old flames, I mean the ones on my old proto (prototype) boards. It was the era when they came out with those "new-fangled" bipolar transistors. They called them "$40 three wire fuses" in one article. They blew up a lot. Tubes always got hot, but they only 'blew up' when you dropped them on the floor. People grumbled about the change, but eventually transistors caught on. Smaller, lighter, lower power, and, eventually, more reliable: what's not to like?

Dr. T: The same thing happened when CMOS started to become popular for analog designs.

Dave: Sure did. This time it's cost driven. And I think we can thank the computer guys, especially the gaming community. Those guys have pushed processor technology to the limit, and made digital design (in CMOS) ever more popular and cheaper.

Dr. T: Your new design is in a CMOS process, right?

Dave: Yes, see the parallel? I'm not grumbling, but there is a learning curve. I've done a lot of analog bipolar, but CMOS is new to me. Many things are similar, but there are a lot of differences too.

Dr. T: Since you've switched to design and are working in a CMOS process, have any interesting insights popped up?

Dave: Funny you should ask. Actually, yes. There was a surprise just last week. One of the problems I was having related to the distortion in an amplifier stage, Figure 1.

Dr. T: Was it a differential input?

Dave: Yes, with a single-ended output. Over the signal range, the phase response varied more than the spec allowed, and I couldn't fix it.

Figure 1: Video distortions with unbalanced input impedances
(Click on image to enlarge)

Dr. T: You couldn't just throw more current at it?

Dave: No, we were already tight on the power budget so I had to find another way.

Dr. T: So what did you do?

Dave: Well, I banged my head against my computer for a few days, and accused the SPICE simulator of all kinds of improbable things before trying an old bipolar trick. Let me explain. The problem started with a CMOS amplifier with huge input devices. CMOS has less gm (gain) than bipolar, so we often compensate by making the devices very big.

Dr. T: Sounds like the capacitance would get big, too.

Dave: Exactly. The input capacitance of the amp was almost a picofarad (that's big for a high speed video amp).

Dr. T: And we usually compensate with a feedback cap to prevent peaking.

Dave: Right again! But the problem was that the input capacitance changes with signal voltage. The effect was large enough to cause my distortion.

Dr. T: And there was no way to balance it out?

Dave: Not that I could think of at first. We often reduce distortion and control things in IC design by making things ratiometric. That is, one part of the circuit is a simple multiple of another part, and the gain turns out to be the simple ratio.

Dr. T: Sounds like an interesting idea, but how does it work?

Dave: It's like our standard feedback equation where Gain = R_f/R_in. In a chip, both R_f and R_in will vary with temperature and process. In some chips, R_f will be 10 kΩ, and in some it will be 8.756 kΩ, yet we need the gain to be constant.

If we make a resistor from a certain material (p polysilicon or n polysilicon etc) and we make it a certain shape it will end up about 1 kΩ or so. If we make R_f out of 10 of those in series we'll get about 10 kΩ. If we make R_in out of 5 of those in series we'll get about 5 kΩ. That makes our gain 2.

But now notice since R_f and R_in are made out of the same 'unit resistor' the ratio of the resistances is the same (=2) no matter how much the actual resistor value varies. We call that ratiometric, since the effect we're interested in—the gain—depends only of the ratio and not the absolute value of the resistors.

Dr. T: Like the diode ratios in a bandgap.

Dave: Yep! Simple ratios are well-controlled over process, temperature and signal variations. What I finally noticed in this circuit was that the impedance at the minus input to the amp was about 10 kΩ, and the impedance at the positive input was very low, about 100 Ω.

Dr. T: Wait, since this is a CMOS amplifier, aren't both inputs capacitive?

Dave: Yes, but they are driven by a source (the output of the previous stage, probably another transistor) with an output impedance.

Dr. T: Yes, of course. And that creates a node in the circuit.

Dave: I know you love to talk about nodes, so let's hear the spiel.

Dr. T: The signal path flows through a circuit through a sequence of nodes. Every node has the ability to store charge (capacitance) and to dissipate that charge (resistance). The product of these gives the time constant of the node. The inversion of that time constant is the pole (in radians/second).

Dave: Exactly. So our amplifier has poles at both input nodes, one due to feedback impedance and input C, and the other due to source impedance and input C.

Dr. T: And those aren't the same?

Dave: That's the problem. If they were the same, then they tend to cancel out.

Dr. T: Oh yes, the complex version of R_f/R_in is Z_f/Z_in if they are the same the gain is unity (flat).

Dave: So the feedback loop was actually 'correcting' for a varying time constant made up of the 10 kΩ (R₁ and R₂ in parallel fixed), the feedback C₁ (fixed) and the input C (varies). But there was no such effect at the positive input. If the feedback network had a phase lag, the amp would respond by having a phase lead at the output.

Dr. T: And that's because the feedback equation inverts the effect of the feedback network.

Dave: Yes. I'll leave the math to our interested readers, but a low pass in the feedback makes a high pass at the output and a high pass in the feedback makes a low pass in the output. The interesting one is that a delay in the feedback makes an advance in the output . So with enough delay lines and op amps I could predict the stock market tomorrow!

Dr. T: I think there's something wrong with your logic there

Dave: Of course. If you push the concept to extremes, the whole thing becomes unstable . So I won't be getting rich anytime soon. However, over small ranges, the effect works very well. A small phase delay in the feedback makes a small phase lead in the output.

Dr. T: But what you really wanted, though, was the same effect at both inputs.

Dave: I needed to add resistance to the input so its RC product matched the feedback RC product, Figure 2.

Dave: Yes, with a single-ended output. Over the signal range, the phase response varied more than the spec allowed, and I couldn't fix it.

Figure 2: Compensating for varying input capacitance
(Click on image to enlarge)

Dr. T: That almost sounds like balancing DC currents in a bipolar op amp. You need to make the equivalent resistances the same at both inputs to minimize the offset.

Dave: That's it! If I balanced the RC delays at both the positive and negative inputs, then, as the C varied with signal, both RC's would vary and effectively cancel each other out. So I put a series R from the signal to the positive input (with a C across it as in the feedback R). Now I have the same effect happening at both inputs, and just like the DC case, they cancel. My distortion almost disappeared, (Figure 3)! Problem solved.

Dave: Yes, with a single-ended output. Over the signal range, the phase response varied more than the spec allowed, and I couldn't fix it.

Figure 3: Video distortion reduction with balanced input impedances
(Click on image to enlarge)

Dr. T: Hmmm you could have reduced the resistors to, say, 100 Ω to reduce the effect, right?

Dave: Yes. But then the amp has to drive 100 Ω resistors instead of 10 kΩ resistors that takes a lot more power.

Dr. T: And all that delay doesn't it affect the amp stability?

Dave: It would if we let it get big enough. This is a video application and we are cancelling phase shifts of a few degrees maximum. And notice that the actual solution is at the input, not the feedback, so it doesn't adversely affect stability.

Dr. T: Sounds like we covered all bases.

Dave: Yes. And in the end we have to simulate the circuit over all conditions and signals to make sure we got the math right.

Dr. T: I like it! A little creative analysis gives a solution without a power penalty. Cool. And you are using a well known DC solution to solve a new AC problem. Very cool.

Moral: Keep learning. You never know when an old or new circuit trick will bail you out!

Previous "dialogues" in this series:

• True engineers solve problems using the tools at hand: building a bandgap reference
• Avoiding op amp "motor boating" (also known as "inadvertent positive feedback")
• A bypass-capacitor dialogue peels back the layers, Part 1
• A bypass-capacitor dialogue peels back the layers, Part 2: The theory of ground relativity
• A bypass-capacitor dialogue peels back the layers, Part 3: Continuing the discussion on layout considerations

Other related articles by Dave Ritter:

• Desert Island Design: Bridging the (filter) gap without software
• Desert Island Design: Bridging the (band) gap without software

About the authors
Dave Ritter grew up outside of Philadelphia in a house that was constantly being embellished with various antennas and random wiring. By the age of 12, his parents refused to enter the basement anymore, for fear of lethal electric shock. He attended Drexel University back when programming required intimate knowledge of keypunch machines. His checkered career wandered through NASA where he developed video-effects machines and real-time disk drives. Finally seeing the light, he entered the semiconductor industry in the early 90's. Dave has about 20 patents, some of which are actually useful. He has found a home at Intersil Corporation as a principal applications engineer. Eternally youthful and bright of spirit, Dave feels privileged to commit his ideas to paper for the entertainment and education of his soon to be massive readership.

Tamara Schmitz grew up in the Midwest, finding her way west with an acceptance letter to Stanford University. After collecting three EE degrees (BS, MS, and PhD), she taught analog circuits and test-development engineering as an assistant professor at San Jose State University. With 8 years of part-time experience in applications engineering, she joined industry full-time at Intersil Corporation as a principal applications engineer. In twenty years, she hopes to be as eternally youthful as Dave. .

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