TIA Input Z: Infinite… or Zero? What is it,really?
Bruce Trump - October 8, 2012
What is the input impedance of a transimpedance amplifier (TIA)? Infinite? Zero? No, whatis it really? Nothing is really zero or infinite, right? The answer might surprise you—worthunderstanding, even if you don’t use TIAs. After all, an inverting amplifier is just a TIA with aninput resistor, right?
The transimpedance amplifier converts an input current to a voltage and is often used tomeasure small currents, (figure 1). With an ideal op amp, infinite gain and bandwidth, theinput impedance of a TIA is zero. Feedback of the op amp maintains V1 at virtual ground,creating a zero impedance. Like an ammeter, an ideal current measurement circuit shouldhave zero impedance.
We’re still working on the ideal op amp, so until then, what’s the input Z with finite gain-bandwidth product? Some reasoning and 8th-grade algebra reveal an interesting result.
The open-loop gain vs. frequency for the OPA314 is shown in figure 2. As with most op ampstoday, the gain follows a constant -20dB/decade slope through a wide frequency range—overfive decades for this general purpose device. Its gain-bandwidth is 3MHz, so the gain at anyfrequency along this range is fapproximately 3MHz/f.
Manipulating the factors that we know (shown in yellow boxes) yields the result. Z isproportional to RF and frequency and inversely proportional to GBP. But, hey… Z
proportional to frequency? That feels much like a basic circuit element—an inductor. Theimpedance of an inductor is 2fL, so we can calculate an equivalent input inductance of theTIA.
Neat, huh? Or, maybe you already knew it. Over a wide frequency range the input sourcesees a simple inductor as a load. We want this inductance to be as low as possible in mostapplications. RF is generally dictated by the transimpedance gain required, so that leaveshigher op amp GBP as the only way to reduce this inductance. Put this observation to workand it might give additional insight into the behavior of photodiode or current transformercircuits (often used with TIAs).
There’s nothing really new here. Various synthetic inductor circuits using amplifiers have
been around a very long time but you may not have made the connection to TIAs or invertingamplifiers. Deeper understanding and creativity often come from making these connections.Most important is the simple observation on the input voltage of an op amp. We so oftenwant to think of the differential input voltage of an op amp as zero—the infinite gain
assumption. But across a wide frequency range, it certainly is not. The simple relationship ofGBP, frequency and output voltage provides an easy way to understand how the inputvoltage varies with frequency.
Now, a couple of provisos: This is a small-signal analysis. If you drive the op amp withenough amplitude and high enough frequency, the op amp will slew and voltage at V1 willincrease. And this model assumes a simple -20dB/decade roll-off of the open-loop responseof the op amp. Some op amps may have twitches in the open loop response that have aminor affect on the simple Gain = GBP/f model.
An additional thought exercise… could we refine the inductance model to include the effect offinite DC open-loop gain?
Thanks for reading and comments are most welcome.Bruce thesignal@list.ti.com Index to all The Signal blogs.
