Bootstrapping - John Dunn, Consultant, Ambertec, P.E., P.C.

Bootstrapping circuits can provide useful impedance increases and control of the impedances that are presented by garden variety components.

This circuit immediately below allows the effective shunt impedance (shunt resistance) from the right-hand end of C1 to ground to be increased well above the resistance value of R1 itself.

With C1 as a 0.1 µF and R1 as a 100K, I actually got the low-frequency corner of this high-pass circuit to be at a lower frequency than that of the AC coupled mode of the Tektronix scope I was using.

My circuit had beaten the Tektronix one. What a thrill that was!  

 

You can bootstrap capacitances too which can let you partially cancel out some non-removable shunt capacitance might be dealing with, say perhaps from a few dozen feet of coaxial cable. 

 
If you make the gain value "A" variable, this circuit will behave as a controllable (variable) shunt capacitance in the sense that a varactor would be such a controllable variable capacitance.

Just don't go too far with this. If you bootstrap so much that the net capacitance becomes a negative value, you'll have made an oscillator.

Comments

[george storm]

Regarding bootstrapping the input resistance: when do such corcuits have a known and non-removable input resistance? Otherwise we do better either to buy a large-value resistor or to bootstrap using a follower with a potential divider at the output.

BTW, the AC-mode time constant of most 'scopes is set not by technology, but so that the user does not perceive an excessive delay before the signal settles. (Sorry to be a spoil-sport here)

[John Dunn]

That R1 was an RN55 or RN60 style (I forget which) and that style of film resistor didn't come in values of high enough ohms for the purpose at hand. Bootstrapping was the answer to that.

[Fred Floru]

Below is a link to an IC that uses a similar technique to boost just the common impedance of a differential amplifier.

http://thatcorp.com/datashts/THAT_1200-Series_Datasheet.pdf

[Sergio Franco]

Rewriting as Rin = R2/(R2/R1-R3/R4) better evidences that Rin depends on the difference between two resistance ratios. In applications where these ratios are designed to be very close to each other, a slight mismatch may alter Rin significantly, making it even infinite or negative, depending on the direction of the mismatch. So, even though the circuit is elegant in theory, one has to be aware of this feature when applying it in practice. Regards,

Sergio Franco

http://online.sfsu.edu/~sfranco/BookAnalog/AnalogJacket.pdf