—A transimpedance amplifier for use with a pro- posed ultra-linear current-output DAC was designed, imple- mented, and experimentally verified. The target precision was a signal-to-noise-and-distortion ratio (SINAD) of 122 dBFS, or 20 effective number of bits (ENOB), over a bandwidth of 100 kHz. Experimental verification was limited by the available measurement instrumentation, but the target was met. Index Terms—Measurement, measurement techniques, pre- cision measurements, operational amplifiers, low-noise ampli- fiers, current measurement. I. Introduction Several integrated CMOS devices present a current- based output signal, such as photo-detectors and digital- to-analog converters (DACs). These devices do not behave as ideal current sources. To minimize distortion, they should ideally be connected to zero ohm at ground, or a fixed, potential [1]. The best off-the-shelf DACs can yield approximately 16 ENOB at audio frequencies (20 Hz to 20 kHz) [2]. The Authors are working to improve this performance to more than 18 ENOB from DC to 100 kHz. The most promising DAC topologies produce a current output, and to reliably measure the performance of these experimental DACs, a low-noise, low-distortion output stage is required that at the same time is able to uphold the output impedance and voltage requirements; hence a transimpedance amplifier (TIA) [1] is required. This also enables it to interface most standard instrumentation, typically requiring a voltage signal. The proposed TIA enables 20 ENOB with a 100 kHz bandwidth, whilst providing ideal output con- ditions for the DAC. II. Transimpedance Amplifier Fig. 1 shows a TIA configuration using an operational amplifier (opamp), complete with typical noise sources [3]. The gain of the amplifier is A=Rf, and the value of Rfis set according to the magnitude of the signal current and the desired output voltage of the application. The feedback capacitor Cflimits the bandwidth of the feedback network. Limiting the bandwidth mitigates stability issues and reduces high-frequency noise. The cut- off frequency is given by fc= 1=2RfCf. The current noise of the opamp itself, iOAn, contributes directly as an input noise current. The input capacitance Cinis the capacitance at the input node of the opamp, typically consisting of parasitic capacitances. Cincauses + enIin iOAn Cin VoutRfvRnoiseCf Rout1 ClfRout2Voutlp Fig. 1. Bandwidth-limited transimpedance amplifier with noise sources and impedance-matching low-pass filter on the output the input voltage noise enof the opamp to generate an input current noise [3]. As a noise density it is expressed asinc=enCin!=enCin2f; increasing proportionally with frequency. The feedback resistor Rfalso generates current noise iRnoiseconsisting of Johnson noise and excess noise [4]: iRnoise =q 4kBT =R f+iexcess Here kBis Boltzmanns constant and Tis temperature; iexcessis excess noise. This is also known as 1=f-noise and depends on the technology used to manufacture the resistor and the current flowing through it [4]. The output impedance of the TIA is the same as the output impedance of the opamp, which is ideally Rout;opamp = 0 . To match the impedance with a 50 cable, a passive RC filter is added on the output with Rout1+Rout2+Rout;opamp = 50 . By adding Clfand choosing Rout1 Rout2, the greatest portion of the Johnson noise becomes band-limited. Note that both Rout resistors will contribute excess noise (not shown in Fig. 1), but this it is negligible compared to the excess noise of Rfsince it is not amplified. III. Design The amplifier is designed for an input current of 20 mA peak-to-peak, and an output voltage of 5 Vpeak-to-peak (7:07 Vrms). Hence the gain is Rf= 5 V =20 mA = 250 . To achieve a bandwidth of 100 kHz, a feedback loop cut- off frequency of 200 kHzwas chosen combined with a low- pass filter frequency of 100 kHz. Hence Cf= 1=2Rffc 3:2 nF. The input capacitance Cinis estimated to be 7 pF, based on the chosen connectors and the PCB layout. The opamp OPA1612 from Texas Instruments was selected for its low noise and low distortion. It has en= 1:1 nV=p HzandiOAn= 1:7 pA=p Hzat1 kHz. 979-8-3503-6104-9/24/$31.00 ©2024 IEEE 1011021031041051 nV10 nV100 nV Frequency (Hz)Noise ( V=p Hz)Noise-floor ( =1:74µV) Measured ( =1:94µV) Simulated ( =1:1µV) vRnoise Rfb(=0:7µV) vexcess Rfb(=0:5µV)Fig. 2. Output noise Given the above, the noise terms iOAnandincbecome insignificant compared to the noise from the feedback resistor iRnoise. IV. Results SPICE simulations of the TIA were performed, using the manufacturer provided opamp model and a worst- case noise-index of -30 dB for the excess noise of Rf. The opamp is the dominant source of harmonic distortion, but this is unfortunately not modeled in the provided SPICE models. An approximate value of -128 dB can however be derived from the datasheet. The prototype TIA was measured with a National Instruments PXI-5922 oscilloscope, using a sampling fre- quency of 500 kHzin order to achieve maximum resolution and the lowest possible noise floor for the instrument. The noise-floor was measured by connecting directly to the output of the TIA with the input of the TIA shorted to signal ground. To measure harmonic distortion, a SWG03 precision Waveform Generator by the Czech Metrology Institute was connected through a 44 precision resistor to generate an input current for the TIA. The resulting output voltage was measured with the oscilloscope. Fig. 2 shows the simulated and measured noise of the TIA, as well as the noise floor of the oscilloscope. The standard deviation for the entire 10 Hzto250 kHz bandwidth is given for each series. Fig. 3 shows both the output spectrum of the TIA and the waveform generator connected directly to the PXI-5922 oscilloscope. V. Discussion Noise simulations in Fig. 2 show that the excess noise of the feedback resistor dominate at lower frequencies, up to around 1 kHz. Between that frequency and the cut-off at100 kHz, the Johnson noise of the feedback resistor is dominating. Elevated noise levels at 50 Hzand some spikes in the 10 kHzto40 kHzare observed, likely due to the power 10-210-1100101102-150-100-500Power (dB)TIA THD: -89.58dBF 2 34Fundamental Harmonics DC and Noise (excluded) 10-210-1100101102 Frequency (kHz)-150-100-500Power (dB)Signal generator THD: -88.50dBF 2 34Fundamental Harmonics DC and Noise (excluded)Fig. 3. Measured harmonic distortion supply. These may be eliminated by using better supply decoupling and/or a differential configuration. The instrument noise floor is too high to accurately measure the noise performance of the TIA. At lower frequencies, the TIA may perform better than the sim- ulations due to the worst-case assumption of the Noise Index. At high-frequencies, the instrument noise floor is significantly higher than in the simulations; as this effect was not included. Total harmonic distortion (THD) measurements in Fig. 3 likely do not reflect the performance of the TIA, but rather that of the signal generator. The minor difference in THD as well as the noise shape at higher frequencies may be explained by the effect of loading the signal generator with the shunt resistor. VI. Conclusion and Outlook TheexperimentalresultsshowthattheTIAhasequalor lower amounts of noise and distortion than the measure- ment setup. The signal-to-noise-and-distortion (SINAD) ratio of the TIA with the measured noise floor and THD of -128 dBFS from the opamp datasheet is then 20 log (7 :07 V=(1:94µV + 2 :83µV)) 123dBFS indicating that the TIA is exceeding our target of 20 ENOB. An improved measurement setup must be devised in order to measure these extremely low levels of noise and distortion.