# How to design a 180 degree phase inverter for the feedback?

I am currently working on a multi-stage wideband amplifier (80-110 GHz) design with the goal of having 5-6 dB for each stage. The transistor that I am using has the transit frequency around 300 GHz (so we are not limited by the device). My objective is to use a capacitance and a phase inverter for the feedback to widen the bandwidth, something like this:

(Image source - Figure 5 from paper: Katayama, Kosuke et al. “An 80–106 GHz CMOS amplifier with 0.5V supply voltage.2017 IEEE Radio Frequency Integrated Circuits Symposium (RFIC) (2017): 308-311.)

Without feedback, the maximum gain that I could get was around 3 dB (+- 1.5dB) around the desired frequency range (in other frequencies less than 80 GHz, the gain was around 6-8 dB). Now, when I tried to add a feedback with a capacitor (calculated to be 38fF using the formulas and technique described here: https://www.researchgate.net/publication/280204342_Theory_of_gain_and_stability_of_small-signal_amplifiers_with_lossless_reciprocal_feedback

Then, I tried to add the phase inverter with a simple 90 degree transmission line (microstrip line) that I got with Linecalc tool from ADS (with Zo as 50 ohms), the gain curve almost flat around 80-110 GHz but the gain (S21) is negative (around -5 or -4 dB).

I tried the following:

1. I noticed that S11 was far away (around 5-j*x) and the feedback signal is not flowing because of the impedance mismatch so, we tried to improve the matching at the input (S11) to 50 ohms by adding a series inductor (around 400-1000 pH) - it did not improve the performance.
2. Then I tuned the Width, length of the phase inverter (Microstrip line) and the capacitor values. (almost flat around gain around 4-5 dB) but I don't know the logic when I tune.

Could you please suggest some ideas to improve the gain in wideband (without tuning) with this technique?