# A Low-Loss Circuit with High-Pass Low-Pass Broadband Flat Negative Group Delay Characteristics
## 1 Introduction  
Group delay is an important technical indicator in identifying whether a communication system is in good condition, and distortion of group delay can cause some problems, such as increased system error rates. The negative group delay circuit, as a method of balancing group delay, has received a lot of attention.  
Since the discovery of the theory of negative group delay, scholars have conducted extensive research on negative group delay circuits and proposed different circuit structures with negative group delay to meet different needs, such as the crab shape, Li type, etc. [1, 2, 3, 4]. This includes lumped parameter circuits and microstrip line circuits. After proposing different circuit structures, scholars conducted theoretical analyses on negative group delay circuits [5, 6, 7]. At the same time, scholars have attempted to apply different negative group delay circuits in different fields, such as filters [8, 9], non-Foster capacitors [10], cables [11], and improving array antenna performance [12, 13, 14] to eliminate the positive group delay generated by signals passing through communication systems.  
Over time, scholars have found that there are usually significant fluctuations in circuit performance when negative group delay occurs. Therefore, the question of how to obtain a flat negative group delay to achieve ultra-low bit error rates in communication has become an important direction of negative group delay research [15]. In Ref. [16], a negative group delay circuit composed of microstrip lines is proposed. With a negative group delay of \(-1.11\) ns and an insertion loss of \(9.75\) dB, the flat NGD bandwidth is \(6.1\%\) and the group delay fluctuation is \(11.5\%\). In the study of flat negative group delay circuits, many scholars use a fluctuation of \(8\%\) as the standard [17, 18], with a negative group delay of about \(-0.5\) ns and insertion loss of over \(15\) dB under this standard. Similarly, many scholars usea fluctuation of 20% as the standard, which, as shown in [19], has a negative group delay of \(-0.2\) ns and an insertion loss of 14 dB.  
These flat circuit structures can usually only achieve one function. In Ref. [9], a circuit structure with three functions--low pass, high pass, and band pass--is proposed. However, the negative group delay that it achieves is not smooth, and, in research on flatness, it has significant insertion losses. Therefore, it is necessary to develop a multifunctional and low-loss flat negative group delay circuit.  
This study proposes a flat negative group delay low-loss circuit that can achieve both high-pass and low-pass functions by changing the circuit component parameters. This article consists of four sections. The second section mainly describes the circuit structure and theoretically analyzes the circuit transfer function and group delay. It explores the impact of delay component parameters on the circuit when implementing a high-pass or low-pass negative group. The third section presents the circuit theory and simulation results and compares them with other research results to demonstrate that the circuit has the advantages of high-pass and low-pass flat negative group delay. The final section presents the conclusions of the study.