## Optimize Your HF2TA Transimpedance Amplifier Settings

Users of the HF2TA transimpedance amplifier should always be aware of the trade-off between the transimpedance gain and the 3-dB roll-off bandwidth of the amplifier. (Hint: Since the HF2 software release 12.08, the bandwidth is also specified in the HF2TA gain drop-down list in ziControl.) However, there are other pitfalls to watch out for when using the HF2TA transimpedance amplifier which may not be so obvious to every user. In this blog, I will describe two issues one should be aware of when using the HF2TA transimpedance amplifier: Gain Saturation and Gain-to-DUT-Impedance Ratio. But before that, let us first look at how a transimpedance amplifier works.

### Transimpedance Amplifier and Virtual Ground

The diagram below is a very basic representation of a transimpedance amplifier driven by a source. In this example, when an excitation voltage vs is applied, a current will flow through the device-under-test ZDUT into the node vx. The node vx is called the ac virtual ground because in an ideal amplifier circuit, the ac voltage measured at this node is always zero due to the feedback action of the amplifier with an open loop gain AOL. In reality, the AC voltage at the node vis never really zero. In generally, the bigger the open loop gain AOL of the amplifier is, the closer the node  vx will be to the ideal virtual ground. Let us suppose that the ideal virtual ground exists. Then, the current flowing through ZDUT must also flow through the feedback resistor RT  i.e. Kirchhoff’s Current Law. Consequently, the output voltage of the transimpedance amplifier vwill be the current multiplied by the value of RT. The resistor RT is therefore called the transimpedance gain since the signal current is converted into voltage with a gain of RT. Notice in the same diagram that the source has an output resistance of 50 Ω as well as the input of the amplifier to the virtual ground vx. The 50 Ω resistors are intentionally placed to match the characteristic impedance of the (BNC) cables.

### Gain Saturation

When selecting a large value of the transimpedance gain RT, it is possible to saturate the transimpedance amplifier output without triggering the over voltage warning of the HF2LI lock-in amplifier or the HF2IS impedance spectroscope. The consequence is false amplitude with a distorted waveform (i.e. square wave). This phenomenon is illustrated in the oscilloscope screenshot below. This occurrence is not always obvious to the user because no warning light will appear in ziControl. And this type of gain saturation can result in erroneous amplitude readings. This saturation usually happens when the input signal current is large (e.g. a combination of large vand small ZDUT). A good practice is always to check the oscilloscope in ziControl. Otherwise as a rule thumb, the following table can serve as a reference to determine the maximum gain before saturation occurs. AC coupling can also help if there is a large DC current component. It must be said that if current is large, then only small gain is required. In any case, the maximum input current of the HF2TA transimpedance amplifier is ±10 mA.

### Gain-to-DUT-Impedance Ratio

It was previously mentioned that the concept of AC virtual ground where the open loop gain AOL determines the quality of this virtual ground. This is only partially true. As a matter of fact if one is measuring an impedance ZDUT, the ratio of ZDUT and the selected transimpedance gain Rcan also affect the quality of the AC virtual ground. Without going into the full derivation, the voltage vx in the first diagram can estimated by the equation below: Let us suppose that AOL is 1000 and vs is 1 V. If  the ratio of the total input impedance including ZDUT and RT is at least 1, then the AC virtual ground vwill be smaller than 1 mV. This is not too bad given the input voltage amplitude. However, if the ratio is smaller than, let us say 0.01, then vwill be close to 100 mV. One can no longer call the node vx a true virtual ground. The current measured will of course be incorrect. In short, the gain Rshould be kept under the impedance ZDUT if possible to minimize measurement error. This is especially important at frequencies beyond 1 MHz where the open loop gain AOL starts to drop below 1000.

In this blog we discussed the basic operation of the HF2TA transimpedance amplifier and how to have an optimized its setting. Besides respecting the gain vs bandwidth criteria, HF2TA transimpedance amplifier users should also take precautions when it comes to selecting the transimpedance gain in order to avoid amplifier saturations as well as unintentional measurement errors.